Mimo communication system having deterministic communication path and antenna arrangement method therfor

ABSTRACT

A MIMO communication system has deterministic channels between the transmission side where a plurality of transmission antennas are arranged and the reception side where a plurality of reception antennas are arranged and used in a line-of-sight environment. The system includes channel matrix calculation processing means for calculating a channel matrix for constructing orthogonal channels as the channel on a transmission or reception side or both of the transmission and reception sides. The plurality of transmission antennas and plurality of reception antennas constituting the channel matrix are horizontally arranged with respect to the ground.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Divisional Application of U.S. patent applicationSer. No. 14/035,406, filed Sep. 24, 2013, which is ContinuationApplication of U.S. patent application Ser. No. 12/452,942, filed onJan. 29, 2010, now U.S. Pat. No. 8,571,125, which is based on and claimspriority from International Application No. PCT/JP2008/063893, filed onAug. 1, 2008, and Japanese Patent Application No. 2007-201773, filed onAug. 2, 2007, the entire contents of which is incorporated herein byreference.

TECHNICAL FIELD

The present invention relates to a space-division multiplexing method(hereinafter, referred to as “MIMO (Multiple-Input/Multiple-Output)” ina Line-Of-Sight (LOS) environment and, more particularly to a MIMOcommunication system having deterministic channels like a fixed pointmicrowave communication system, and an antenna arrangement methodtherefore.

BACKGROUND ART

A technique using a MIMO has become popular in the field of wirelesscommunication, and the MIMO itself is becoming no longer a newtechnology. However, conventional techniques using the MIMO mainly focuson a mobile communication, and application of the MIMO to a fixed pointcommunication has not been fully examined. In a mobile communicationradio channels, radio wave coming from a transmission antenna isreflected or scattered according to the surrounding terrain and reachesa receiver in the form of a group of waves, resulting in occurrence offading phenomenon which has been an obstacle to achievement of highquality communication. The MIMO technique in a mobile communication doesnot demonize the fading phenomenon but considers it as environmentalresources with great potential that are inherent in mobile communicationradio propagation. In this point, the MIMO technique is regarded as arevolutionary technique.

Although smaller in the amount of examples than the mobilecommunication, NPL (non-patent literature) 1 discloses consequents ofapplication of such a MIMO technique to a line-of-sight fixed pointradio communication where radio channels are determined. The mobilecommunication as described above deals with channels as a random matrix.On the other hand, the line-of-sight fixed point radio communicationneeds to deal with channels as deterministic channels. The above NPL 1describes, as follows, what effect is produced on a channel matrix Hconstituting channels between transmission and reception antennas as aresult of extension of antenna interval on both the transmission sideand reception side.

H·H ^(H) =n·I _(n)  [Numeral 1]

where n is the number of antennas, H^(H) is the Hermitian transposedmatrix of channel matrix H, and I is a unit matrix, and the phaserotation of a signal with respect to a transmission antenna i andreception antenna k linearly arranged so as to face each other betweenthe transmission side and reception side is set by the following formulaand thereby the transmission and reception antennas can be constitutedby linear antennas.

$\begin{matrix}{\frac{\pi}{n} \cdot \left\lbrack {i - k} \right\rbrack^{2}} & \left\lbrack {{Numeral}\mspace{14mu} 2} \right\rbrack\end{matrix}$

Assuming that n=2, the channel matrix H is represented by the followingformula.

$\begin{matrix}{H_{\max} = \begin{bmatrix}1 & j \\j & 1\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 3} \right\rbrack\end{matrix}$

In this case, an antenna configuration satisfying the condition ofNumeral 1 is possible. NPL 1 describes that when the condition ofNumeral 1 is satisfied, channel capacity in the MIMO configurationbecomes maximum by H_(max). That is, an increase in channel capacitybased on the MIMO can be achieved not only in a mobile communicationenvironment that is subject to reflection or scattering but also in adeterministic line-of-sight communication environment.

Now, considering a case where such a deterministic line-of-sight MIMO isapplied to a small fixed point microwave communication system. Ingeneral, the small fixed point microwave communication system uses afrequency band of several GHz to several tens of GHz, which correspondsto several mm to several cm in terms of wavelength. Therefore, asignificant phase rotation may occur due to movement in the antennadirection highly sensitive to a subtle change of weather condition suchas wind or surrounding temperature. Under such a condition, it isdifficult to ensure the deterministic channel matrix. Note thattheoretical analysis to be described later analytically reveals that theabove increase in channel capacity can be achieved even when such adisplacement in the highly sensitive antenna direction occurs.

In the MIMO technique, a plurality of independent signals aretransmitted/received at the same frequency band. Therefore, signalseparation/detection is necessary. As a means for realizing this, thereis a known a method (hereinafter, referred to as SVD method) based onmatrix calculation using a unitary matrix which is obtained by SingularValue Decomposition (SVD). Assume that feedback information forconstruction of the unitary matrix can ideally be send from a receptionend to transmission end in the SVD method. In this case, even if theabove displacement in the highly sensitive antenna direction occurs, theunitary matrix acts so as to compensate for the displacement. As aresult, large capacity fixed point microwave communication can berealized based on the MIMO. However, the above feedback information mayincrease system overhead. In addition, it is necessary to prepare areverse channel for exchanging the feedback information. Note that amodeling of a channel matrix H to be described later performs analysisincluding the displacement in the highly sensitive antenna direction.

When the singular value analysis is carried out for the line-of-sightfixed channels where channels are deterministic, there exists aninter-antenna position at which an eigenvalue is a multiplicitycondition to generate a singular point. Although the singular-value isuniquely determined, singular vectors are not unique. This state, whichis particularly analytically troublesome, may cause significanttransition of the singular vectors. However, by utilizing thisphenomenon, various configurations can be possible. Various examples ofconfigurations that take advantage of the characteristics will bedescribed in detail later.

As a major problem in the deterministic line-of-sight MIMO, there is aproblem that carrier synchronization between antennas must be achievedon the transmission side or reception side in the above conventionalmethod. That is, the phase between a plurality of antennas on thetransmission side or reception side needs to be equal or needs to have aconstant phase difference.

On the other hand, in the fixed point microwave communication system,antenna interval must be widened in view of a frequency to be used.Correspondingly, radio devices including local oscillators are installednear antennas. That is, the problem of the necessity of achievement ofcarrier synchronization between antennas imposes severe restriction onconstruction of the fixed point microwave communication system.

CITATION LIST Non-Patent Literature

-   {NPL 1} P. F. Driessen and GJ. Foschini, “On the Capacity Formula    for Multiple Input-Multiple Output Wireless Channels: A Geometric    Interpretation”, IEEE Transactions on Communications, Vol. 47, No.    2, February 1999, pp. 173-176

SUMMARY OF INVENTION Technical Problem

Assume that virtual orthogonal channels based on the MIMO that satisfythe above severe restriction imposed on the construction of the fixedpoint microwave communication system has been achieved. However, in thecase where a reflected wave other than the direct wave is present in theline-of-sight channels, the orthogonality of the virtual orthogonalchannels for MIMO formation cannot be maintained due to the presence ofthe reflected wave.

The present invention has been made in view of the above problems, andan object of the present invention is to provide a MIMO communicationsystem having deterministic channels capable of both increasing thechannel capacity by applying the MIMO to deterministic line-of-sightchannels like a fixed point microwave communication system andmaintaining the orthogonality of the virtual orthogonal channels forMIMO even if a reflected wave other than the direct wave is present inthe line-of-sight channels, and an antenna arrangement method for theMIMO communication system.

Another object of the present invention is to provide a MIMOcommunication system having deterministic channels capable of bothoffering performance equivalent to a conventional SVD method withoutfeedback information that needs to be sent from a reception end totransmission end for construction of a unitary matrix in the SVD methodand maintaining the orthogonality of the virtual orthogonal channels forMIMO even if a reflected wave other than the direct wave is present inthe line-of-sight channels, and an antenna arrangement method for theMIMO communication system.

Still another object of the present invention is to provide a MIMOcommunication system having deterministic channels capable of bothsolving the problem of the necessity of achievement of carriersynchronization between antennas which imposes severe restriction onconstruction of the fixed point microwave communication system andmaintaining the orthogonality of the virtual orthogonal channels forMIMO even if a reflected wave other than the direct wave is present inthe line-of-sight channels, and an antenna arrangement method for theMIMO communication system.

Still another object of the present invention is to provide a MIMOcommunication system having deterministic channels capable of bothoffering performance equivalent to an SVD method even under thecondition that it is difficult to ensure a deterministic channel matrixdue to a significant phase rotation caused by movement in the antennadirection highly sensitive to a subtle change of weather condition suchas wind or surrounding temperature and maintaining the orthogonality ofthe virtual orthogonal channels for MIMO even if a reflected wave otherthan the direct wave is present in the line-of-sight channels, and anantenna arrangement method for the MIMO communication system.

Solution to Problem

To solve the above problems, in a first MIMO communication system havingdeterministic channels between the transmission side where a pluralityof transmission antennas are arranged and the reception side where aplurality of reception antennas are arranged and used in a line-of-sightenvironment and an antenna arrangement method for the MIMO communicationsystem, the MIMO communication system includes a channel matrixcalculation processing means for calculating a channel matrix forconstructing orthogonal channels as the channel on a transmission orreception side or both of the transmission and reception sides, whereinthe plurality of transmission antennas and plurality of receptionantennas constituting the channel matrix are horizontally arranged withrespect to the ground.

In a second MIMO communication system and an antenna arrangement methodtherefor having deterministic channels between the transmission sidewhere a plurality of transmission antennas are arranged and thereception side where a plurality of reception antennas are arranged andused in a line-of-sight environment and an antenna arrangement methodfor the MIMO communication system, the MIMO communication systemincludes a channel matrix calculation processing means for calculating achannel matrix for constructing orthogonal channels as the channel on atransmission or reception side or both of the transmission and receptionsides, wherein the plurality of transmission antennas and plurality ofreception antennas constituting the channel matrix are verticallyarranged with respect to the ground, and antenna height from the groundis made an integral multiple of the antenna interval.

In a third MIMO communication system having deterministic channelsbetween the transmission side where a plurality of transmission antennasare arranged and the reception side where a plurality of receptionantennas are arranged and an antenna arrangement method for the MIMOcommunication system, the MIMO communication system includes a channelmatrix calculation processing means for constructing orthogonal channelsas the channels by setting geometric parameters of the channelsconcerning antenna distance so that the eigenvalue of the channel matrixbecomes a multiplicity condition and performing, on the transmission orreception side, matrix calculation using a unitary matrix constitutedbased on singular vectors obtained from the eigenvalue or singularvectors obtained from the linear combination of eigenvectors, whereinthe plurality of transmission antennas and plurality of receptionantennas constituting the channels are horizontally arranged withrespect to the ground.

In a fourth MIMO communication system and an antenna arrangement methodtherefor having deterministic channels between the transmission sidewhere a plurality of transmission antennas are arranged and thereception side where a plurality of reception antennas are arranged andan antenna arrangement method for the MIMO communication system, theMIMO communication system includes a channel matrix calculationprocessing means for constructing orthogonal channels as the channels bysetting geometric parameters of the channels concerning antenna distanceso that the eigenvalue of the channel matrix becomes a multiplicitycondition and performing, on the transmission or reception side, matrixcalculation using a unitary matrix constituted based on singular vectorsobtained from the eigenvalue or singular vectors obtained from thelinear combination of eigenvectors, wherein the plurality oftransmission antennas and plurality of reception antennas constitutingthe channels are vertically arranged with respect to the ground, andantenna height from the ground is made an integral multiple of theantenna interval.

Advantageous Effects of Invention

As described above, according to the first MIMO communication systemhaving deterministic channels and an antenna arrangement methodtherefor, even if a reflected wave other than the direct wave is presentduring line-of-sight communication, it is possible to ensureorthogonality.

According to the second MIMO communication system having deterministicchannels and an antenna arrangement method therefor, even if a reflectedwave other than the direct wave is present during line-of-sightcommunication, it is possible to ensure orthogonality in an antennaconfiguration where space saving is achieved due to vertical arrangementof the antennas.

According to the third MIMO communication system having deterministicchannels and an antenna arrangement method therefor, even if a reflectedwave other than the direct wave is present during line-of-sightcommunication, it is possible to ensure orthogonality with the maximumcapacity.

According to the fourth MIMO communication system having deterministicchannels and an antenna arrangement method therefor, even if a reflectedwave other than the direct wave is present during line-of-sightcommunication, it is possible to ensure orthogonality with the maximumcapacity in an antenna configuration where space saving is achieved dueto vertical arrangement of the antennas.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 A view showing a configuration example of a MIMO communicationsystem according to an exemplary embodiment of the present invention,where an SVD method where antenna distance is arbitrarily set andfluctuation of antenna position in the highly sensitive antennadirection is taken into consideration.

FIG. 2 A view showing an example of the MIMO communication systemaccording to a first example of the present invention, where calculationbased on a unitary matrix V is performed only on the transmission side.

FIG. 3 A view showing an example of the MIMO communication systemaccording to a second example of the present invention, where matrixcalculation is performed only on the transmission side and where virtualorthogonal channels have different values.

FIG. 4 A view showing an example of the MIMO communication systemaccording to a third example of the present invention, where calculationbased on a unitary matrix is performed only on the reception side andwhere local oscillators are provided independently for respectiveantennas on the transmission side.

FIG. 5 A view showing an example of the MIMO communication systemaccording to a fourth example of the present invention, wherecalculation based on a unitary matrix is performed only on the receptionside and where local oscillators are provided independently forrespective antennas both on the transmission and reception sides.

FIG. 6 A view showing an example of the MIMO communication systemaccording to a fifth example of the present invention, where matrixcalculation is performed only on the reception side, where virtualorthogonal channels have different values, and where local oscillatorsare provided independently for respective antennas both on thetransmission and reception sides.

FIG. 7 A view showing an example of the MIMO communication systemaccording to a sixth example of the present invention, where threeantennas are installed respectively on the transmission and receptionsides, and where local oscillators are provided independently forrespective antennas both on the transmission and reception sides.

FIG. 8 A view showing an example of the MIMO communication systemaccording to a seventh example of the present invention, where fourantennas are installed respectively on the transmission and receptionsides, and where local oscillators are provided independently forrespective antennas both on the transmission and reception sides.

FIG. 9 A view showing comparison between SNRs of virtual orthogonalchannels based on respective methods in terms of antenna distance.

FIG. 10 A view showing a configuration example in which antennadistances differ from each other between transmission and receptionsides.

FIG. 11 A view obtained by modeling the lower half of the verticallysymmetric channel configuration of FIG. 10.

FIG. 12 A view showing communication capacity in the case of FIG. 10where antenna distances differ from each other between transmission andreception sides.

FIG. 13 A view showing a configuration example in which antennaarrangement between the transmission and reception sides is formed in adiamond shape along the antenna arrangement direction.

FIG. 14 A view showing a configuration example in which antennaarrangement between the transmission and reception sides is formed in adiamond shape along the antenna arrangement direction and wherecalculation based on a unitary matrix is performed only on receptionside.

FIG. 15 A view showing a case where antenna arrangement is formed in agiven geometric form.

FIG. 16 A view showing a line-of-sight microwave propagation model(three-ray model).

FIG. 17 A view showing an ideal MIMO operating condition in aline-of-sight two-ray model.

FIG. 18 A view showing a case where MIMO antennas are horizontallyarranged.

FIG. 19 A view showing a case where MIMO antennas are horizontallyarranged, as viewed from above (upper part) and edge-on (lower part).

FIG. 20 A view showing an application example of a configuration inwhich matrix calculation is performed only on transmission side.

FIG. 21 A view showing a case where MIMO antennas are verticallyarranged.

FIG. 22 A view showing a case where MIMO antennas are verticallyarranged, as viewed from above (upper part) and edge-on (lower part).

FIG. 23 A view showing a mirror image model of a configuration in whichMIMO antennas are vertically arranged.

FIG. 24 A view showing an analysis model of a configuration in whichMIMO antennas are vertically arranged.

FIG. 25 A view showing a case where MIMO antennas are horizontallyarranged under actual condition.

FIG. 26 A view showing a case where irregular reflecting objects exist.

FIG. 27 A view showing an arbitrary i-th irregular reflection model.

FIG. 28 A graph showing eigenvalues on the virtual orthogonal channels.

REFERENCE SIGNS LIST Explanation of Reference Symbols

-   101: Matrix calculation processing section based on unitary matrix V-   102: Frequency conversion section-   103: Mixer-   104: Local oscillator-   105: Mixer-   106: Fixed antenna section-   107: Fixed antenna section-   108: Frequency conversion section-   109: Mixer-   110: Local oscillator-   111: Mixer-   112: Matrix calculation processing section based on unitary matrix U-   201: Matrix calculation processing section based on unitary matrix V-   202: Fixed antenna section-   203: Fixed antenna section-   301: Matrix calculation processing section based on matrix V-   302: Fixed antenna section-   303: Fixed antenna section-   401: Pilot signal generation section-   402: Frequency conversion section-   403: Mixer-   404: Local oscillator-   405: Local oscillator-   406: Modeling of phase noise caused due to absent of synchronization    between carriers-   407: Mixer-   408: Fixed antenna section-   409: Fixed antenna section-   410: Matrix calculation processing section based on unitary matrix U-   501: Pilot signal generation section-   502: Frequency conversion section-   503: Mixer-   504: Local oscillator-   505: Local oscillator-   506: Modeling of phase noise caused due to absent of synchronization    between carriers-   507: Mixer-   508: Fixed antenna section-   509: Fixed antenna section-   510: Frequency conversion section-   511: Mixer-   512: Local oscillator-   513: Local oscillator-   514: Modeling of phase noise caused due to absent of synchronization    between carriers-   515: Mixer-   516: Pilot detection section-   517: Matrix calculation processing section based on unitary matrix U-   601: Pilot signal generation section-   602: Frequency conversion section-   603: Mixer-   604: Local oscillator-   605: Local oscillator-   606: Modeling of phase noise caused due to absent of synchronization    between carriers-   607: Mixer-   608: Fixed antenna section-   609: Fixed antenna section-   610: Frequency conversion section-   611: Mixer-   612: Local oscillator-   613: Local oscillator-   614: Modeling of phase noise caused due to absent of synchronization    between carriers-   615: Mixer-   616: Pilot detection section-   617: Matrix calculation processing section based on matrix U-   2001: Transmission station-   2002: Reception station 1-   2003: Reception station 2

DESCRIPTION OF EXEMPLARY EMBODIMENTS

An exemplary embodiment of the present invention will be described withreference to the accompanying formulas and accompanying drawings. Beforethat, a theoretical reasoning for the fact that channel capacity in theMIMO configuration becomes maximum even with deterministic line-of-sightchannels will be explained.

The channel capacity of virtual orthogonal channels based on the MIMOconfiguration is represented by eigenvalues of respective paths. Then,eigenvalue analysis is performed for an antenna configuration as shownin FIG. 1. The following modeling, whose antenna configuration andreference symbols are shown in FIG. 1, takes the displacement in thehighly sensitive antenna direction into consideration. Although a casewhere two antennas are used will be described for convenience, the samecalculation may be applied regardless of the number of antennas.

In FIG. 1, a MIMO communication system used in a line-of-sightenvironment has deterministic channels between the transmission side(transmitter or transmission end) where a plurality of transmissionantennas are arranged and reception side (receiver or reception end)where a plurality of reception antennas are arranged. H in FIG. 1denotes a channel matrix, and V (V11, V12, V21, V22) and U (U11, U12,U21, U22) denote a transmission side unitary matrix and a reception sideunitary matrix, respectively. U^(H) and V^(H) denote the Hermitiantransposed matrixes of U and V, respectively, and Λ^(1/2) denotes asingular value diagonal matrix.

The transmission side includes a matrix calculation processing section101 based on unitary matrix V, a frequency conversion section 102(including mixers 103, 105, and a local oscillator 104), and a fixedantenna section 106 (including two antennas (transmission antennas)).The reception side includes a fixed antenna section 107 (including twoantennas (reception antennas)), a frequency conversion section 108(including mixers 109, 111, and a local oscillator 110), and a matrixcalculation processing section 112 based on unitary matrix U. S₁ and S₂are transmission signals transmitted from the two antennas on thetransmission side, and r₁ and r₂ are reception signals transmitted fromthe two antennas on the reception side.

Further, as geometric parameters concerning the communication channelantenna distance, R denotes a distance between transmission andreception antennas, d_(T) denotes a transmission antenna elementinterval, d_(R) denotes reception antenna element interval, and Δθdenotes angle of a diagonal channel with respect to an opposing channelbetween the transmission and reception antennas. Φ denotes phase shiftof a transmission signal S₂ caused by a position variation of atransmission antenna (see FIG. 1), and γ denotes wavelength.

In the eigenvalue analysis for the antenna configuration of FIG. 1, thedistance decay and common phase shift based on a transmitter-receiverdistance R are determined by relative phase shift and therefore can beignored. The channel difference between R and diagonal channel of angleΔθ is represented by the following formula using the geometricparameters (R, Δθ, d_(T), and d_(R)).

$\begin{matrix}\begin{matrix}{{R \cdot \left( {1 - {\cos ({\Delta\theta})}} \right)} \approx {R \cdot \left( \frac{({\Delta\theta})^{2}}{2} \right)}} \\{= {R \cdot \left( {\frac{1}{2}\left( \frac{d_{R}}{R} \right)^{2}} \right)}} \\{= {\frac{d_{R}^{2}}{2R}\because\frac{d_{R}}{R}}} \\{= {\tan ({\Delta\theta})}} \\{{\approx ({\Delta\theta})},{{{at}\mspace{14mu} d_{T}} = d_{R}}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 4} \right\rbrack\end{matrix}$

Accordingly, phase rotation a resulting from the channel difference isrepresented by the following formula using γ.

$\begin{matrix}{\alpha = {{2{\pi \left( \frac{d_{R}^{2}}{2R} \right)}\text{/}\gamma} = {\frac{\pi}{\gamma} \cdot \frac{d_{R}^{2}}{R}}}} & \left\lbrack {{Numeral}\mspace{14mu} 5} \right\rbrack\end{matrix}$

Incidentally, assuming that RF frequency=30 GHz (γ=(3×10⁸)[m/s]/(30×10⁹) [Hz], R=5000 m, d_(T)=d_(R)=5 m, a is calculated by thefollowing formula.

$\begin{matrix}{\alpha = {{\frac{\pi}{\gamma} \cdot \frac{d_{R}^{2}}{R}} = {{\frac{\pi}{\left( {3 \cdot 10^{8}} \right)\text{/}\left( {30 \cdot 10^{9}} \right)} \cdot \frac{5^{2}}{5000}} = \frac{\pi}{2}}}} & \left\lbrack {{Numeral}\mspace{14mu} 6} \right\rbrack\end{matrix}$

Therefore, channel matrix H considering phase shift Φ based on theposition variation (see FIG. 1) of a transmission antenna fortransmitting a signal s₂ is represented by the following formula.

$\begin{matrix}{H = \begin{bmatrix}1 & {^{{- j}\; \alpha} \cdot ^{j\Phi}} \\^{{- j}\; \alpha} & {1 \cdot ^{j\; \Phi}}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 7} \right\rbrack\end{matrix}$

Accordingly, assuming that H·H^(H)(H^(H) is the Hermitian transposedmatrix of H) is Ω, the following formula is obtained.

$\begin{matrix}\begin{matrix}{\Omega = {H^{H} \cdot H}} \\{= {\begin{bmatrix}1 & ^{j\; \alpha} \\{^{j\; \alpha} \cdot ^{{- j}\; \Phi}} & ^{{- j}\; \Phi}\end{bmatrix} \cdot \begin{bmatrix}1 & {^{{- j}\; \alpha} \cdot ^{j\; \Phi}} \\^{- {j\alpha}} & ^{j\; \Phi}\end{bmatrix}}} \\{= \begin{bmatrix}2 & {^{j\; \Phi}\left( {^{j\; \alpha} + ^{{- j}\; \alpha}} \right)} \\{^{- {j\Phi}}\left( {^{j\; \alpha} + ^{{- j}\; \alpha}} \right)} & 2\end{bmatrix}} \\{= \begin{bmatrix}2 & {{2 \cdot \cos}\; {\alpha \cdot ^{j\; \Phi}}} \\{{2 \cdot \cos}\; {\alpha \cdot ^{{- j}\; \Phi}}} & 2\end{bmatrix}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 8} \right\rbrack\end{matrix}$

Accordingly, eigenvalues λ₁ and λ₂ representing channel capacity of thevirtual orthogonal channels can be calculated as follows.

$\begin{matrix}\begin{matrix}{\left| \begin{matrix}{2 - \lambda} & {{2 \cdot \cos}\; {\alpha \cdot ^{j\; \Phi}}} \\{{2 \cdot \cos}\; {\alpha \cdot ^{- {j\Phi}}}} & {2 - \lambda}\end{matrix} \right| = {\lambda^{2} + 4 - {4\lambda} - {4\cos^{2}\alpha}}} \\{= {\lambda_{2} - {4\lambda} - {4\sin^{2}\alpha}}} \\{= {0\therefore\lambda}} \\{= {2 \pm \sqrt{4 - {4\sin^{2}\alpha}}}} \\{= {2 \pm {2\cos \; \alpha}}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 9} \right\rbrack\end{matrix}$

A calculation result of Numeral 9 is shown in FIG. 28. The analysisresult of FIG. 28 shows a case where unit power is transmitted per oneantenna and, therefore, channel capacity is double the number ofantennas. It should be noted here that the modeling used in the abovecalculation includes a displacement in the highly sensitive antennadirection. Despite this, the displacement component does not appear in aresult of the eigenvalue representing a final channel capacity. That is,an increase in the channel capacity is possible by MIMO even in theline-of-sight fixed point radio communication where radio channels aredetermined. The channel capacity is determined by the antenna distancenot relevant to the highly sensitive antenna displacement.

A case where two antennas are used has been described above. In thefollowing, a case where three or more antennas are used will bedescribed.

The phase rotation resulting from the channel difference betweendiagonal channels of antenna elements linearly arranged on thetransmission and reception sides is obtained from [Numeral 5] and,assuming that antenna element interval is a common value of d, the phaserotation is represented by the following formula.

$\begin{matrix}{\frac{\pi}{\gamma} \cdot \frac{d^{2}}{R}} & \left\lbrack {{Numeral}\mspace{14mu} 10} \right\rbrack \\{{\frac{\pi}{\gamma} \cdot \frac{d^{2}}{R}} = {{\frac{\pi}{3}\therefore\frac{d^{2}}{R}} = \frac{\gamma}{3}}} & \left\lbrack {{Numeral}\mspace{14mu} 11} \right\rbrack\end{matrix}$

Thus, when the antenna element interval d and transmitter-receiverdistance R are defined so that the above Numeral 11 is satisfied and aconfiguration in which three antennas are used is considered, a channelmatrix H₃ represented by the following formula can be obtained.

$\begin{matrix}{H_{3} = \begin{bmatrix}1 & ^{{- j}\frac{\pi}{3}} & ^{{- j}\; 4\frac{\pi}{3}} \\^{{- j}\frac{\pi}{3}} & 1 & ^{{- j}\frac{\pi}{3}} \\^{{- j}\; 4\frac{\pi}{3}} & ^{{- j}\frac{\pi}{3}} & 1\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Accordingly, assuming that H₃·H₃ ^(H)(H₃ ^(H) is the Hermitiantransposed matrix of H) is Ω, the following formula is obtained.

$\begin{matrix}\begin{matrix}{\Omega = {H_{3}^{H} \cdot H_{3}}} \\{= {\begin{bmatrix}1 & ^{j\frac{\pi}{3}} & ^{j\; 4\frac{\pi}{3}} \\^{j\frac{\pi}{3}} & 1 & ^{j\frac{\pi}{3}} \\^{{j4}\frac{\pi}{3}} & ^{j\frac{\pi}{3}} & 1\end{bmatrix} \cdot \begin{bmatrix}1 & ^{{- j}\frac{\pi}{3}} & ^{{- j}\; 4\frac{\pi}{3}} \\^{{- j}\frac{\pi}{3}} & 1 & ^{{- j}\frac{\pi}{3}} \\^{{- j}\; 4\frac{\pi}{3}} & ^{{- j}\frac{\pi}{3}} & 1\end{bmatrix}}} \\{= \begin{bmatrix}3 & 0 & 0 \\0 & 3 & 0 \\0 & 0 & 3\end{bmatrix}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 13} \right\rbrack\end{matrix}$

Thus, it can be understood that three eigenvalues corresponding to thechannel capacity of the virtual orthogonal channels are all “3” and thatthe entire channel capacity is three times the number of antennas.

Similarly, antenna element interval d and transmitter-receiver distanceR are defined so that the following formula is satisfied and aconfiguration in which four antennas are used is considered.

$\begin{matrix}{{\frac{\pi}{\gamma} \cdot \frac{d^{2}}{R}} = {{\frac{\pi}{4}\therefore\frac{d^{2}}{R}} = \frac{\gamma}{4}}} & \left\lbrack {{Numeral}\mspace{14mu} 14} \right\rbrack\end{matrix}$

Thus, a channel matrix H₄ represented by the following formula can beobtained.

$\begin{matrix}{H_{4} = \begin{bmatrix}1 & ^{{- j}\frac{\pi}{4}} & ^{{- j}\; 4\frac{\pi}{4}} & ^{{- j}\; 9\frac{\pi}{4}} \\^{{- j}\frac{\pi}{4}} & 1 & ^{{- j}\frac{\pi}{4}} & ^{{- j}\; 4\frac{\pi}{4}} \\^{{- j}\; 4\frac{\pi}{4}} & ^{{- j}\frac{\pi}{4}} & 1 & ^{{- j}\frac{\pi}{4}} \\^{{- j}\; 9\frac{\pi}{4}} & ^{{- j}\; 4\frac{\pi}{4}} & ^{{- j}\frac{\pi}{4}} & 1\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 15} \right\rbrack\end{matrix}$

Accordingly, assuming that H₄·H₄ ^(H)(H₄ ^(H) is the Hermitiantransposed matrix of H) is Ω, the following formula is obtained.

$\begin{matrix}{\Omega = {{H_{4}^{H} \cdot H_{4}} = {\cdot \begin{bmatrix}1 & ^{j\frac{\pi}{4}} & ^{j\; 4\frac{\pi}{4}} & ^{j\; 9\frac{\pi}{4}} \\^{j\frac{\pi}{4}} & 1 & ^{j\frac{\pi}{4}} & ^{{j4}\frac{\pi}{4}} \\^{{j4}\frac{\pi}{4}} & ^{j\frac{\pi}{4}} & 1 & ^{j\frac{\pi}{4}} \\^{j\; 9\frac{\pi}{4}} & ^{j\; 4\frac{\pi}{4}} & ^{j\frac{\pi}{4}} & 1\end{bmatrix} \cdot {\quad{\begin{bmatrix}1 & ^{{- j}\frac{\pi}{4}} & ^{{- j}\; 4\frac{\pi}{4}} & ^{{- j}\; 9\frac{\pi}{4}} \\^{{- j}\frac{\pi}{4}} & 1 & ^{{- j}\frac{\pi}{4}} & ^{{- j}\; 4\frac{\pi}{4}} \\^{{- j}\; 4\frac{\pi}{4}} & ^{{- j}\frac{\pi}{4}} & 1 & ^{{- j}\frac{\pi}{4}} \\^{{- j}\; 9\frac{\pi}{4}} & ^{{- j}\; 4\frac{\pi}{4}} & ^{{- j}\frac{\pi}{4}} & 1\end{bmatrix} = \begin{bmatrix}4 & 0 & 0 & 0 \\0 & 4 & 0 & 0 \\0 & 0 & 4 & 0 \\0 & 0 & 0 & 4\end{bmatrix}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 16} \right\rbrack\end{matrix}$

Thus, it can be understood from the above formula that four eigenvaluescorresponding to the channel capacity of the virtual orthogonal channelsare all “4” and that the entire channel capacity is four times thenumber of antennas.

That is, it can be understood that even when the number of antennasexceeds 2, the channel capacity of deterministic line-of-sight channelsis increased to an extent corresponding to the number of antennas whichis equivalent to the maximum capacity of MIMO. Note that although a casewhere two antennas are used will be described for convenience in thefollowing examples, it goes without saying that the same is applied to acase where the number of antennas exceeds 2.

Next, as a signal separation/detection method in MIMO, a method(hereinafter, referred to as SVD method) based on matrix calculationusing a unitary matrix which is obtained by Singular Value Decompositionwill be described. In the SVD method, matrix calculation using a unitarymatrix V on the transmission side and matrix calculation using a unitarymatrix U on the reception side are required. In order to perform thematrix calculation using the unitary matrix V, feedback information forconstruction of the unitary matrix needs to be sent from the receptionend to transmission end.

An exemplary embodiment of the present invention will be described indetail below with reference to the accompanying formulas and drawings.

In FIG. 1, transmission signals processed by a transmission side matrixcalculation processing section 101 based on the unitary matrix V arefrequency converted into signals of a radio frequency by thetransmission side frequency conversion section 102 including the localoscillator 104, and mixers 103 and 105 and then transmitted from thefixed antenna section 106 including a plurality of antennas as s₁ ands₂. The notation of the s₁ and s₂ is based on equivalent basebandrepresentation.

It should be noted here that carrier synchronization between antennas isachieved by a local oscillation signal supplied from one localoscillator 104 to the mixers 103 and 105. This results from arestriction on a space-division multiplexing fixed point microwavecommunication system that deterministic channels are determined based onthe phase difference between paths. However, as described later, thelocal oscillator 104 may be provided independently for each antenna.

The signals thus transmitted are received by a reception side fixedantenna section 107 including a plurality of antennas as r₁ and r₂. Thenotation of the r₁ and r₂ is based on equivalent basebandrepresentation. The reception signals r₁ and r₂ are frequency convertedinto signals of a baseband frequency by the reception side frequencyconversion section 108 including the local oscillator 110 and mixers 109and 111 and then processed by the reception side matrix calculationprocessing section 112 based on the unitary matrix U, whereby signalseparation/detection in MIMO is completed.

It should be noted here that carrier synchronization between antennas isachieved by a local oscillation signal supplied from one localoscillator 110 to the mixers 109 and 111. This results from arestriction on a space-division multiplexing fixed point microwavecommunication system that deterministic channels are determined based onthe phase difference between paths. Also in this case, as describedlater, the local oscillator 110 may be provided independently for eachantenna as in the case of the transmission end. The antennas to be usedare not particularly limited and may be a parabola antenna or a hornantenna.

Next, a method of calculating the unitary matrixes V and U using thefollowing channel matrix H considering a given antenna distance andhighly sensitive antenna displacement will concretely be described withreference to formulas.

Channel matrix H of line-of-sight channels used here is represented bythe following formula.

$\begin{matrix}{{H = \begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\; \Phi}} \\^{{- j}\; \alpha} & {1 \cdot ^{j\Phi}}\end{bmatrix}}{{where};}{{\alpha = {{\frac{\pi}{\gamma} \cdot \frac{d_{R}^{2}}{R}}\left( {{{at}\mspace{14mu} d_{T}} = d_{R}} \right)}},{\Phi;}}{{phase}\mspace{14mu} {change}\mspace{14mu} {caused}\mspace{14mu} {by}\mspace{14mu} {displacement}}} & \left\lbrack {{Numeral}\mspace{14mu} 17} \right\rbrack\end{matrix}$

In the following description, singular value diagonal matrix Λ^(1/2)based on the eigenvalue is represented by the following formula.

$\begin{matrix}{\Lambda^{1/2} = {\begin{bmatrix}\sqrt{2 + {2\cos \; \alpha}} & 0 \\0 & \sqrt{2 - {2\cos \; \alpha}}\end{bmatrix} = {\quad{\begin{bmatrix}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & 0 \\0 & {2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix} = {\quad{\begin{bmatrix}\left( {^{j\frac{\alpha}{2}} + ^{{- j}\frac{\alpha}{2}}} \right) & 0 \\0 & {- {j\left( {^{j\frac{\alpha}{2}} - ^{{- j}\frac{\alpha}{2}}} \right)}}\end{bmatrix}\because\left\{ \begin{matrix}{{1 + {\cos \; \alpha}} = {2{\cos^{2}\left( \frac{\alpha}{2} \right)}}} \\{{1 - \cos}\; = {2{\sin^{2}\left( \frac{\alpha}{2} \right)}}}\end{matrix} \right.}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 18} \right\rbrack\end{matrix}$

Hereinafter, the unitary matrix V and unitary matrix U are calculatedusing the above channel matrix H in the order mentioned.

[Unitary Matrix V]

From [Numeral 17], the channel matrix H is represented by the followingformula.

$\begin{matrix}{H = \begin{bmatrix}1 & {^{{- j}\; \alpha} \cdot ^{j\; \Phi}} \\^{{- j}\; \alpha} & {1 \cdot ^{j\; \Phi}}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 19} \right\rbrack\end{matrix}$

It is assumed that an eigenvector corresponding to the channel matrix His represented by the following formula.

$\begin{matrix}\begin{bmatrix}a \\b\end{bmatrix} & \left\lbrack {{Numeral}\mspace{14mu} 20} \right\rbrack\end{matrix}$

In this case, the following formula is satisfied.

$\begin{matrix}{\Omega = {{H^{H} \cdot H} = \begin{bmatrix}2 & {{2 \cdot \cos}\; {\alpha \cdot ^{j\; \Phi}}} \\{{2 \cdot \cos}\; {\alpha \cdot ^{{- j}\; \Phi}}} & 2\end{bmatrix}}} & \left\lbrack {{Numeral}\mspace{14mu} 21} \right\rbrack\end{matrix}$

Accordingly, the following formula can be obtained.

$\begin{matrix}{{\begin{bmatrix}{2 - \lambda} & {{2 \cdot \cos}\; {\alpha \cdot ^{j\; \Phi}}} \\{{2 \cdot \cos}\; {\alpha \cdot ^{{- j}\; \Phi}}} & {2 - \lambda}\end{bmatrix} \cdot \begin{bmatrix}a \\b\end{bmatrix}} = 0} & \left\lbrack {{Numeral}\mspace{14mu} 22} \right\rbrack\end{matrix}$

From the [Numeral 22], the following formula can be obtained.

$\begin{matrix}{a = {{\frac{{{- 2} \cdot \cos}\; {\alpha \cdot ^{j\; \Phi}}}{2 - \lambda}b} = {{\frac{\cos \; {\alpha \cdot ^{j\; \Phi}}}{{\pm \cos}\; \alpha}b} = {{{{\pm ^{j\; \Phi}} \cdot b}\because\lambda} = {2 \pm {2\cos \; \alpha}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 23} \right\rbrack \\{\mspace{79mu} {{\Omega \cdot v} = {\lambda \cdot v}}} & \left\lbrack {{Numeral}\mspace{14mu} 24} \right\rbrack\end{matrix}$

When both sides of the above formula are multiplied by V^(H) from theleft, the following formula is obtained.

v ^(H) ·Ω·v=λ[Numeral 25]

Then, orthogonal Vs are collected and the following formula is obtained.

V ^(H) ·Ω·V=Λ=Λ∴Ω=V·Λ·V ^(H)  [Numeral 26]

H=U·Λ ^(1/2) ·V ^(H)  [Numeral 27]

From the above formula, the following [Numeral 28] is satisfied.

Ω=H ^(H) ·H=V·Λ ^(1/2) ·U ^(H) ·U·Λ ^(1/2) ·V ^(H) =V·Λ·V ^(H)  [Numeral28]

Accordingly, the eigenvectors each represented the following [Numeral29] are collected and thereby [Numeral 30] is obtained.

$\begin{matrix}{v = \begin{bmatrix}a \\{{\pm a} \cdot ^{{- j}\; \Phi}}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 29} \right\rbrack \\{V = \begin{bmatrix}x & y \\{x \cdot ^{{- j}\; \Phi}} & {{- y} \cdot ^{{- j}\; \Phi}}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 30} \right\rbrack\end{matrix}$

Here, the following [Numeral 31] is set as a special solutionconsidering normalization and orthogonality.

$\begin{matrix}{{x = \frac{- 1}{\sqrt{2}}},{y = \frac{1}{\sqrt{2}}}} & \left\lbrack {{Numeral}\mspace{14mu} 31} \right\rbrack\end{matrix}$

From [Numeral 31], the following formula is obtained.

$\begin{matrix}{V = {{\begin{bmatrix}\frac{- 1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\\frac{- ^{{- j}\; \Phi}}{\sqrt{2}} & \frac{- ^{{- j}\; \Phi}}{\sqrt{2}}\end{bmatrix}\therefore V^{H}} = \begin{bmatrix}\frac{- 1}{\sqrt{2}} & \frac{- ^{j\; \Phi}}{\sqrt{2}} \\\frac{1}{\sqrt{2}} & \frac{- ^{j\; \Phi}}{\sqrt{2}}\end{bmatrix}}} & \left\lbrack {{Numeral}\mspace{14mu} 32} \right\rbrack\end{matrix}$

[Unitary Matrix U]

$\begin{matrix}{\Omega^{\prime} = {{H \cdot H^{H}} = {{\begin{bmatrix}1 & {^{{- j}\; \alpha} \cdot ^{j\; \Phi}} \\^{{- j}\; \alpha} & {1 \cdot ^{j\; \Phi}}\end{bmatrix} \cdot \begin{bmatrix}1 & ^{j\; \alpha} \\{^{j\; \alpha} \cdot ^{{- j}\; \Phi}} & {1 \cdot ^{{- j}\; \Phi}}\end{bmatrix}} = {\quad\begin{bmatrix}2 & {{2 \cdot \cos}\; \alpha} \\{{2 \cdot \cos}\; \alpha} & 2\end{bmatrix}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 33} \right\rbrack\end{matrix}$

It is assumed that an eigenvalue u is represented by the following[Numeral 34] based on the above [Numeral 33].

$\begin{matrix}\begin{bmatrix}a \\b\end{bmatrix} & \left\lbrack {{Numeral}\mspace{14mu} 34} \right\rbrack\end{matrix}$

In this case, the following formula is satisfied.

$\begin{matrix}{{\begin{bmatrix}{2 - \lambda} & {{2 \cdot \cos}\; \alpha} \\{{2 \cdot \cos}\; \alpha} & {2 - \lambda}\end{bmatrix} \cdot \begin{bmatrix}a \\b\end{bmatrix}} = 0} & \left\lbrack {{Numeral}\mspace{14mu} 35} \right\rbrack\end{matrix}$

From the above, the following formula is obtained.

$\begin{matrix}{a = {{\frac{{{- 2} \cdot \cos}\; \alpha}{2 - \lambda}b} = {{\frac{\cos \; \alpha}{{\pm \cos}\; \alpha}b} = {{{\pm b}\because\lambda} = {2 \pm {2\cos \; \alpha}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 36} \right\rbrack \\{{\Omega^{\prime} \cdot u} = {\lambda \cdot u}} & \left\lbrack {{Numeral}\mspace{14mu} 37} \right\rbrack\end{matrix}$

When both sides of the above formula are multiplied by u^(H) from theleft, the following formula is obtained.

U ^(H) ·Ω′·u=λ  [Numeral 38]

Then, orthogonal Us are collected and the following formula is obtained.

U ^(H) ·Ω′·U=Λ∴Ω′=U·Λ·U ^(H)  [Numeral 39]

Accordingly, the eigenvectors each represented by the following [Numeral40] are collected to obtain [Numeral 41].

$\begin{matrix}{u = \begin{bmatrix}a \\{\pm a}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 40} \right\rbrack \\{U = \begin{bmatrix}x & y \\x & {- y}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 41} \right\rbrack\end{matrix}$

Here, the following [Numeral 42] is set as a special solutionconsidering normalization and orthogonality.

$\begin{matrix}{{x = \frac{- ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}}},{y = \frac{j \cdot ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}}}} & \left\lbrack {{Numeral}\mspace{14mu} 42} \right\rbrack\end{matrix}$

From [Numeral 42], the following formula is obtained.

$\begin{matrix}{U = {{\begin{bmatrix}\frac{- ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}} & \frac{j \cdot ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}} \\\frac{- ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}} & \frac{{- j} \cdot ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}}\end{bmatrix}\therefore U^{H}} = \begin{bmatrix}\frac{- ^{j\frac{\alpha}{2}}}{\sqrt{2}} & \frac{- ^{j\frac{\alpha}{2}}}{\sqrt{2}} \\\frac{{- j}\; ^{j\frac{\alpha}{2}}}{\sqrt{2}} & \frac{j \cdot ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}}\end{bmatrix}}} & \left\lbrack {{Numeral}\mspace{14mu} 43} \right\rbrack\end{matrix}$

For confirmation of the unitary matrixes V and U obtained by the abovecalculation, singular value decomposition of the channel matrix H isperformed with V and U.

[Singular Value Decomposition of H=U·Λ·V^(H)]

$\begin{matrix}{\begin{matrix}{{H = U}{{\cdot \Lambda^{1/2} \cdot V^{H}} = {\begin{bmatrix}\frac{- ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}} & \frac{j \cdot ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}} \\\frac{- ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}} & \frac{{- j} \cdot ^{{- j}\frac{\alpha}{2}}}{\sqrt{2}}\end{bmatrix} \cdot}}} \\{{\begin{bmatrix}\left( {^{j\frac{\alpha}{2}} + ^{{- j}\frac{\alpha}{2}}} \right) & 0 \\0 & {- {j\left( {^{j\frac{\alpha}{2}} - ^{{- j}\frac{\alpha}{2}}} \right)}}\end{bmatrix} \cdot}} \\{\begin{bmatrix}\frac{- 1}{\sqrt{2}} & \frac{- ^{j\Phi}}{\sqrt{2}} \\\frac{1}{\sqrt{2}} & \frac{- ^{j\Phi}}{\sqrt{2}}\end{bmatrix}} \\{= {\begin{bmatrix}\frac{- \left( {1 + ^{- {j\alpha}}} \right)}{\sqrt{2}} & \frac{\left( {1 - ^{- {j\alpha}}} \right)}{\sqrt{2}} \\\frac{- \left( {1 + ^{- {j\alpha}}} \right)}{\sqrt{2}} & \frac{- \left( {1 - ^{- {j\alpha}}} \right)}{\sqrt{2}}\end{bmatrix} \cdot}} \\{{\begin{bmatrix}\frac{- 1}{\sqrt{2}} & \frac{- ^{j\Phi}}{\sqrt{2}} \\\frac{1}{\sqrt{2}} & \frac{- ^{j\Phi}}{\sqrt{2}}\end{bmatrix} = \begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\^{- {j\alpha}} & {1 \cdot ^{j\Phi}}\end{bmatrix}}}\end{matrix}\quad} & \left\lbrack {{Numeral}\mspace{14mu} 44} \right\rbrack\end{matrix}$

Thus, it can be understood that, as in the above example, it is possibleto form orthogonal channels regardless of whether the optimum position(R=5000 m and d_(T)=d_(R)=5 m) is achieved or not.

However, in this case, the transmission qualities of the obtainedvirtual orthogonal channels are proportional from 2^(1/2) and 2^(1/2) to(2+2 cos α)^(1/2) and (2−2 cos α)^(1/2) and therefore differ from eachother. In the block diagram of FIG. 1, virtual orthogonal channels where(2+2 cos α)^(1/2) and (2−2 cos α)^(1/2) denoted by thick arrows havebeen constructed is shown.

It should be noted that the above unitary matrix includes a variation inthe channels caused due to external factors such as a positionalvariation (modeled in FIG. 1) of the antennas highly sensitive to asubtle change of weather condition such as wind or surroundingtemperature. Thus, even when the above displacement in the highlysensitive antenna direction occurs, the unitary matrix acts so as tocompensate for the displacement.

As described later, even in a configuration in which local oscillatorsare provided independently for respective antennas, the phase differenceis modeled into the position variation of the antenna. Therefore, in theconfiguration of this example, the local oscillators may be providedindependently. The feedback information for construction of the V matrixneeds to be sent from the reception end to transmission end in thisconfiguration. However, when a configuration is adopted in which thedisplacement is compensated only on the reception side, it is possibleto eliminate the need to use the feedback information.

General virtual orthogonal channels including a case where theconstructed paths have different widths has been described above. In thefollowing, a singular point where the line-of-sight fixed channels havemultiplicity conditions will be considered.

When the singular value analysis is carried out for the line-of-sightfixed channels where channels are deterministic, there exists aninter-antenna position at which an eigenvalue is a multiplicitycondition to generate a singular point. Although the singular-value isuniquely determined, singular vectors are not unique. This state(Deficient matrix), which is particularly analytically troublesome, maycause significant transition of the singular vectors. However, byutilizing this phenomenon, various configurations can be possible.Various examples of configurations that take advantage of thecharacteristics will be described later. Before that, the principle willbe described.

Here, an inter-antenna position where [Numeral 46] is satisfied with αin [Numeral 45] will be considered.

$\begin{matrix}{\alpha = {{2{{\pi \left( \frac{d^{2}}{2R} \right)}/\gamma}} = {\frac{\pi}{\gamma} \cdot \frac{d^{2}}{R}}}} & \left\lbrack {{Numeral}\mspace{14mu} 45} \right\rbrack \\{^{j\alpha} = {\pm j}} & \left\lbrack {{Numeral}\mspace{14mu} 46} \right\rbrack\end{matrix}$

Hereinafter, ±j is represented as j for simplicity.

The channel matrix H in this state is represented by the followingformula.

$\begin{matrix}{H = \left. \begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\^{- {j\alpha}} & {1 \cdot ^{j\Phi}}\end{bmatrix}\Rightarrow\begin{bmatrix}1 & {{- j} \cdot ^{j\Phi}} \\{- j} & {1 \cdot ^{j\Phi}}\end{bmatrix} \right.} & \left\lbrack {{Numeral}\mspace{14mu} 47} \right\rbrack\end{matrix}$

Here, the following formula is satisfied.

$\begin{matrix}{\Omega^{\prime} = {{H \cdot H^{H}} = {{\begin{bmatrix}1 & {{- j} \cdot ^{j\Phi}} \\{- j} & {1 \cdot ^{j\Phi}}\end{bmatrix} \cdot \begin{bmatrix}1 & j \\{j \cdot ^{- {j\Phi}}} & {1 \cdot ^{- {j\Phi}}}\end{bmatrix}} = \begin{bmatrix}2 & 0 \\0 & 2\end{bmatrix}}}} & \left\lbrack {{Numeral}\mspace{14mu} 48} \right\rbrack\end{matrix}$

Accordingly, from the following [Numeral 49], eigen equation has amultiplicity condition.

$\begin{matrix}{{\begin{matrix}{2 - \lambda} & 0 \\0 & {2 - \lambda}\end{matrix}} = \left( {2 - \lambda} \right)^{2}} & \left\lbrack {{Numeral}\mspace{14mu} 49} \right\rbrack\end{matrix}$

In this case, the following conversion can be possible.

The following formula is satisfied for a given eigenvector u₁ withrespect to eigenvalue λ.

Ω′·u ₁ =λ·u ₁  [Numeral 50]

Similarly, the following formula is satisfied for a given eigenvector u₂with respect to eigenvalue λ.

Ω′·u ₂ =λ·u ₂  [Numeral 51]

Accordingly, the following formula is satisfied for the linear sum ofboth the eigenvalues.

Ω′·(c ₁ ·u ₁ +c ₂ ·u ₂)=λ·(c ₁ ·u ₁ +c ₂ ·u ₂)  [Numeral 52]

Thus, linear sum (c₁·u₁+c₂·u₂) becomes an eigenvector.

It is assumed that an asymptotic eigenvector based on another conditionis set for the multiplicity condition as the following [Numeral 53].

$\begin{matrix}\begin{bmatrix}a \\b\end{bmatrix} & \left\lbrack {{Numeral}\mspace{14mu} 53} \right\rbrack\end{matrix}$

In this case, the following formula is satisfied.

$\begin{matrix}{{\begin{bmatrix}{2 - \lambda} & {{2 \cdot \cos}\; \alpha} \\{{2 \cdot \cos}\; \alpha} & {2 - \lambda}\end{bmatrix} \cdot \begin{bmatrix}a \\b\end{bmatrix}} = 0} & \left\lbrack {{Numeral}\mspace{14mu} 54} \right\rbrack\end{matrix}$

From the above, the following formula is obtained.

$\begin{matrix}{a = {{\frac{{{- 2} \cdot \cos}\; \alpha}{2 - \lambda}b} = {{\frac{\cos \; \alpha}{{\pm \cos}\; \alpha}b} = {{{\pm b}\because\lambda} = {2 \pm {2\mspace{14mu} \cos \; \alpha}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 55} \right\rbrack \\{{\Omega^{\prime} \cdot u} = {\lambda \cdot u}} & \left\lbrack {{Numeral}\mspace{14mu} 56} \right\rbrack\end{matrix}$

When both sides of the above formula are multiplied by u^(H) from theleft, the following formula is obtained.

u ^(H) ·Ω′·u=λ  [Numeral 57]

Then, orthogonal Us are collected and the following formula is obtained.

U ^(H) ·Ω′·U=Λ∴Ω′=U·Λ·U ^(H)  [Numeral 58]

Here, the following formula is satisfied.

Ω′=H·H=U·Λ ^(1/2) ·V ^(H) ·V·Λ ^(1/2) ·U ^(H) =U·Λ·U ^(H)  [Numeral 59]

Accordingly, the above eigenvectors represented by the following[Numeral 60] are collected to obtain [Numeral 61] with normalization andorthogonality taken into consideration.

$\begin{matrix}{u = \begin{bmatrix}a \\{\pm a}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 60} \right\rbrack \\{{u_{1} = \begin{bmatrix}x \\x\end{bmatrix}},{u_{2} = \begin{bmatrix}x \\{- x}\end{bmatrix}}} & \left\lbrack {{Numeral}\mspace{14mu} 61} \right\rbrack\end{matrix}$

Here, when considering sum and difference as linear combination, thefollowing formula is satisfied.

$\begin{matrix}{{{u_{1} + u_{2}} = \begin{bmatrix}{2x} \\0\end{bmatrix}},{{u_{1} - u_{2}} = \begin{bmatrix}0 \\{2x}\end{bmatrix}}} & \left\lbrack {{Numeral}\mspace{14mu} 62} \right\rbrack\end{matrix}$

From the above, the following formula is obtained.

$\begin{matrix}{U = \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 63} \right\rbrack\end{matrix}$

Further, the following formula is satisfied.

$\begin{matrix}{H = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {\quad{\begin{bmatrix}1 & {{- j} \cdot ^{j\Phi}} \\{- j} & {1 \cdot ^{j\Phi}}\end{bmatrix} = {\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix} \cdot \begin{bmatrix}\sqrt{2} & 0 \\0 & \sqrt{2}\end{bmatrix} \cdot V^{H}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 64} \right\rbrack\end{matrix}$

Accordingly, the following formula is satisfied.

$\begin{matrix}{V^{H} = {{\begin{bmatrix}\frac{1}{\sqrt{2}} & 0 \\0 & \frac{1}{\sqrt{2}}\end{bmatrix} \cdot \begin{bmatrix}1 & {{- j} \cdot ^{j\Phi}} \\{- j} & {1 \cdot ^{j\Phi}}\end{bmatrix}} = {\quad\begin{bmatrix}\frac{1}{\sqrt{2}} & \frac{{- j} \cdot ^{j\Phi}}{\sqrt{2}} \\\frac{- j}{\sqrt{2}} & \frac{^{j\Phi}}{\sqrt{2}}\end{bmatrix}}}} & \left\lbrack {{Numeral}\mspace{14mu} 65} \right\rbrack\end{matrix}$

As a trial, when the channel matrix H is calculated using the obtainedU, λ^(1/2), and V^(H), the following formula is satisfied.

$\begin{matrix}{H = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix} \cdot \begin{bmatrix}\sqrt{2} & 0 \\0 & \sqrt{2}\end{bmatrix} \cdot {\quad{\begin{bmatrix}\frac{1}{\sqrt{2}} & \frac{{- j} \cdot ^{j\Phi}}{\sqrt{2}} \\\frac{- j}{\sqrt{2}} & \frac{^{j\Phi}}{\sqrt{2}}\end{bmatrix} = \begin{bmatrix}1 & {{- j} \cdot ^{j\Phi}} \\{- j} & ^{j\Phi}\end{bmatrix}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 66} \right\rbrack\end{matrix}$

As can be seen from [Numeral 66], the channel matrix H is effected.However, this is merely an example, and various decomposition methodscan be considered based on the same approach, depending on the singularpoint corresponding to the multiplicity condition.

Hereinafter, various examples of the present invention will bedescribed.

First Example

As a first example of the present invention, a configuration example inwhich the matrix calculation is performed only on the transmission sidewill be described.

[Singular Value Diagonal Matrix Λ^(1/2)]

In this example, the virtual orthogonal channels have the same value, sothat singular value diagonal matrix Λ^(1/2) is represented by thefollowing formula.

$\begin{matrix}{\Lambda^{1/2} = {\begin{bmatrix}\sqrt{\lambda_{1}} & 0 \\0 & \sqrt{\lambda_{2}}\end{bmatrix} = {\quad{\begin{bmatrix}\sqrt{2 + {2\cos \; \alpha}} & 0 \\0 & \sqrt{2 - {2\cos \; \alpha}}\end{bmatrix} = \begin{bmatrix}\sqrt{2} & 0 \\0 & \sqrt{2}\end{bmatrix}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 67} \right\rbrack\end{matrix}$

[Channel Matrix H]

In this example, the channel matrix H is represented by the followingformula.

$\begin{matrix}{H = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix} \cdot {\quad{\begin{bmatrix}\sqrt{2} & 0 \\0 & \sqrt{2}\end{bmatrix} \cdot {\quad{{\begin{bmatrix}\frac{1}{\sqrt{2}} & \frac{{- j} \cdot ^{j\Phi}}{\sqrt{2}} \\\frac{- j}{\sqrt{2}} & \frac{^{j\Phi}}{\sqrt{2}}\end{bmatrix}\therefore V} = {\quad{{\begin{bmatrix}V_{11} & V_{12} \\V_{21} & V_{22}\end{bmatrix} = {{\begin{bmatrix}\frac{1}{\sqrt{2}} & \frac{j}{\sqrt{2}} \\\frac{j \cdot ^{- {j\Phi}}}{\sqrt{2}} & \frac{^{- {j\Phi}}}{\sqrt{2}}\end{bmatrix}U^{H}} = {\begin{bmatrix}U_{11} & U_{12} \\U_{21} & U_{22}\end{bmatrix} = {\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}{where}}}}};{\alpha = {{2{{\pi \left( \frac{d_{R}^{2}}{2R} \right)}/\gamma}} = {{\frac{\pi}{\gamma} \cdot \frac{d_{R}^{2}}{R}} = \frac{\pi}{2}}}}}}}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 68} \right\rbrack\end{matrix}$

A configuration obtained based on the above result is shown in FIG. 2.

In FIG. 2, transmission signals processed by a transmission side matrixcalculation processing section 201 based on the unitary matrix V aretransmitted from a fixed antenna section 202 including a plurality ofantennas as s₁ and s₂. The notation of the s₁ and s₂ is based onequivalent baseband representation, and the frequency conversionprocessing is omitted here for avoiding complexity.

The signals thus transmitted are received by a reception side fixedantenna section 203 including a plurality of antennas as r₁ and r₂. Thenotation of the r₁ and r₂ is based on equivalent basebandrepresentation, and the frequency conversion processing into a signal ofa baseband frequency is omitted here. The point is that receiving sidematrix calculation processing based on the unitary matrix U is notperformed at all, but all matrix calculations are done on thetransmission side.

As can be seen from [Numeral 68], in the case where the matrixcalculation is performed only on the transmission side, the matrixincludes a variation in the channels caused due to external factors suchas a positional variation (modeled by Φ in FIG. 2) of the antennashighly sensitive to a subtle change of weather condition such as wind orsurrounding temperature. Thus, even when the displacement in the highlysensitive antenna direction occurs, the unitary matrix acts so as tocompensate for the displacement. In this configuration, the feedbackinformation for construction of the V matrix needs to be sent from thereception end to transmission end. The thick arrows of FIG. 2 denotevirtual orthogonal channels in which channel qualities thereof areproportional to 2^(1/2) and 2^(1/2). The antennas to be used are notparticularly limited and may be a parabola antenna or a horn antenna.

Second Example

As a second example of the present invention, a configuration example inwhich the matrix calculation is performed only on the transmission sidein the virtual orthogonal channels having paths with different widthswill be described.

[Singular Value Diagonal Matrix Λ^(1/2)]

In this example, the virtual orthogonal channels have different values,so that singular value diagonal matrix Λ^(1/2) is represented by thefollowing formula.

$\begin{matrix}{\Lambda^{1/2} = {\begin{bmatrix}\sqrt{\lambda_{1}} & 0 \\0 & \sqrt{\lambda_{2}}\end{bmatrix} = {\quad{\begin{bmatrix}\sqrt{2 + {2\cos \; \alpha}} & 0 \\0 & \sqrt{2 - {2\cos \; \alpha}}\end{bmatrix} = {\quad{\begin{bmatrix}{2{\cos \left( \frac{\alpha}{2} \right)}} & 0 \\0 & {2{\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix} = {\quad\begin{bmatrix}\left( {^{j\frac{\alpha}{2}} + ^{{- j}\frac{\alpha}{2}}} \right) & 0 \\0 & {- {j\left( {^{j\frac{\alpha}{2}} - ^{{- j}\frac{\alpha}{2}}} \right)}}\end{bmatrix}}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 69} \right\rbrack\end{matrix}$

[Channel Matrix H]

In the present example, the channel matrix H is represented by thefollowing formula.

$\begin{matrix}{H = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {\begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\^{- {j\alpha}} & {1 \cdot ^{j\Phi}}\end{bmatrix} = {\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix} \cdot {\quad{\begin{bmatrix}\left( {^{j\frac{\alpha}{2}} + ^{{- j}\frac{\alpha}{2}}} \right) & 0 \\0 & {- {j\left( {^{j\frac{\alpha}{2}} - ^{{- j}\frac{\alpha}{2}}} \right)}}\end{bmatrix} \cdot V^{H}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 70} \right\rbrack\end{matrix}$

Accordingly, the following formula is satisfied.

$\begin{matrix}{V^{H} = {\quad{\begin{bmatrix}\left( {^{j\frac{\alpha}{2}} + ^{{- j}\frac{\alpha}{2}}} \right) & 0 \\0 & {- {j\left( {^{j\frac{\alpha}{2}} - ^{{- j}\frac{\alpha}{2}}} \right)}}\end{bmatrix}^{- 1} \cdot {\quad\begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\^{- {j\alpha}} & {1 \cdot ^{j\Phi}}\end{bmatrix}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 71} \right\rbrack\end{matrix}$

Here, the following formula is satisfied.

$\begin{matrix}{{\frac{1}{\left( {^{j\frac{\alpha}{2}} + ^{{- j}\frac{\alpha}{2}}} \right)} = \frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}},{\frac{1}{- {j\left( {^{j\frac{\alpha}{2}} - ^{{- j}\frac{\alpha}{2}}} \right)}} = \frac{1}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}}} & \left\lbrack {{Numeral}\mspace{14mu} 72} \right\rbrack\end{matrix}$

Accordingly, the following formula is obtained.

$\begin{matrix}{V^{H} = {\begin{bmatrix}\frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & 0 \\0 & \frac{1}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix} \cdot {\quad{\begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\^{- {j\alpha}} & {1 \cdot ^{j\Phi}}\end{bmatrix} = \begin{bmatrix}\frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & \frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} \\\frac{^{- {j\alpha}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} & \frac{^{j\Phi}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 73} \right\rbrack\end{matrix}$

Here, the square norm of the vector is represented by the followingformula.

$\begin{matrix}{{\frac{1}{4 \cdot {\cos^{2}\left( \frac{\alpha}{2} \right)}} + \frac{1}{4 \cdot {\sin^{2}\left( \frac{\alpha}{2} \right)}}} = {\frac{4}{16 \cdot {\sin^{2}\left( \frac{\alpha}{2} \right)} \cdot {\cos^{2}\left( \frac{\alpha}{2} \right)}} = \frac{1}{2 \cdot {\sin^{2}(\alpha)}}}} & \left\lbrack {{Numeral}\mspace{14mu} 74} \right\rbrack\end{matrix}$

Thus, the V^(H) is no longer a unitary matrix.

Therefore, in order to calculate the matrix V, inverse matrixcalculation is required.

As a trial, when the channel matrix H is calculated using the obtainedmatrixes U, Λ^(1/2), and V^(H), the following formula is satisfied.

$\begin{matrix}{H = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix} \cdot \begin{bmatrix}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & 0 \\0 & {2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix} \cdot {\quad{\begin{bmatrix}\frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & \frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} \\\frac{^{- {j\alpha}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} & \frac{^{j\kappa}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix} = \begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\^{- {j\alpha}} & {1 \cdot ^{j\Phi}}\end{bmatrix}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 75} \right\rbrack\end{matrix}$

As can be seen from the above, the channel matrix H is effected.

Next, inverse matrix V of V_(H) is considered. A given matrix Arepresented by the following formula is assumed.

$\begin{matrix}{A = \begin{bmatrix}a_{11} & a_{12} \\a_{21} & a_{22}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 76} \right\rbrack\end{matrix}$

The inverse matrix A⁻¹ of the above matrix A is represented by thefollowing formula.

$\begin{matrix}{A^{- 1} = {\frac{1}{{a_{11}a_{22}} - {a_{12}a_{21}}}\begin{bmatrix}a_{22} & {- a_{12}} \\{- a_{21}} & a_{11}\end{bmatrix}}} & \left\lbrack {{Numeral}\mspace{14mu} 77} \right\rbrack\end{matrix}$

Accordingly, the following formula is obtained.

$\begin{matrix}{V = {\begin{bmatrix}\frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & \frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} \\\frac{^{- {j\alpha}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} & \frac{^{j\Phi}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix}^{- 1} = {{\frac{1}{{\frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} \cdot \frac{^{j\Phi}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}} - {\frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} \cdot \frac{^{- {j\alpha}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}}}\begin{bmatrix}\frac{^{j\Phi}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} & {- \frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}} \\{- \frac{^{- {j\alpha}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}} & \frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}\end{bmatrix}} = {{\frac{2 \cdot \left( {2 \cdot {\sin \left( \frac{\alpha}{2} \right)} \cdot {\cos \left( \frac{\alpha}{2} \right)}} \right)}{1 - ^{- {j2\alpha}}}\begin{bmatrix}\frac{1}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} & {- \frac{^{- {j\alpha}}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}} \\{- \frac{^{- {j\alpha}} \cdot ^{- {j\Phi}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}} & \frac{^{- {j\Phi}}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}\end{bmatrix}} = {{\frac{2}{1 - ^{- {j2\alpha}}}\begin{bmatrix}{\cos \left( \frac{\alpha}{2} \right)} & {{- ^{- {j\alpha}}}{\sin \left( \frac{\alpha}{2} \right)}} \\{{- ^{- {j\Phi}}}^{- {j\alpha}}{\cos \left( \frac{\alpha}{2} \right)}} & {^{- {j\Phi}}{\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix}} = {{\frac{2}{^{j\alpha} - ^{- {j\alpha}}}\begin{bmatrix}{^{j\alpha}{\cos \left( \frac{\alpha}{2} \right)}} & {- {\sin \left( \frac{\alpha}{2} \right)}} \\{{- ^{- {j\Phi}}}{\cos \left( \frac{\alpha}{2} \right)}} & {^{- {j\Phi}}^{j\alpha}{\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix}} = {\frac{1}{jsin\alpha}{\quad{{\begin{bmatrix}{^{j\alpha}{\cos \left( \frac{\alpha}{2} \right)}} & {- {\sin \left( \frac{\alpha}{2} \right)}} \\{{- ^{- {j\Phi}}}{\cos \left( \frac{\alpha}{2} \right)}} & {^{- {j\Phi}}^{j\alpha}{\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix} = {\begin{bmatrix}{{- {j}^{j\alpha}}\frac{\cos \left( {\alpha/2} \right)}{\sin \; \alpha}} & \frac{{jsin}\left( {\alpha/2} \right)}{\sin \; \alpha} \\\frac{{j}^{- {j\Phi}}{\cos \left( {\alpha/2} \right)}}{\sin \; \alpha} & \frac{{- {j}^{- {j\Phi}}}^{j\alpha}{\sin \left( {\alpha/2} \right)}}{\sin \; \alpha}\end{bmatrix}{where}}};{\alpha = {{2{{\pi \left( \frac{d_{R}^{2}}{2R} \right)}/\gamma}} = {\frac{\pi}{\gamma} \cdot \frac{d_{R}^{2}}{R}}}}}}}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 78} \right\rbrack\end{matrix}$

A configuration obtained based on the above result is shown in FIG. 3.

In FIG. 3, transmission signals processed by a transmission side matrixcalculation processing section 301 based on the matrix V are transmittedfrom a fixed antenna section 302 including a plurality of antennas as s₁and s₂. The notation of the s₁ and s₂ is based on equivalent basebandrepresentation, and the frequency conversion processing is omitted herefor avoiding complexity.

The signals thus transmitted are received by a reception side fixedantenna section 303 including a plurality of antennas as r₁ and r₂. Thenotation of the r₁ and r₂ is based on equivalent basebandrepresentation, and the frequency conversion processing into a signal ofa baseband frequency is omitted here. The point is that receiving sidematrix calculation processing based on the matrix U is not performed atall, but all matrix calculations are done on the transmission side.

As can be seen from [Numeral 78], in the case where the matrixcalculation is performed only on the transmission side, the matrixincludes a variation between the channels caused due to external factorssuch as a positional variation (modeled by Φ in FIG. 3) of the antennashighly sensitive to a subtle change of weather condition such as wind orsurrounding temperature. Thus, even when the displacement in the highlysensitive antenna direction occurs, the matrix on the transmission sideacts so as to compensate for the displacement. In this configuration,the feedback information for construction of the V matrix needs to besent from the reception end to transmission end. The antennas to be usedare not particularly limited and may be a parabola antenna or a hornantenna.

Thus, it can be understood that it is possible to form orthogonalchannels regardless of whether the optimum position (R=5000 m andd_(T)=d_(R)=5 m) is achieved or not and by the matrix calculationprocessing only on the transmission side.

An application of the configuration in which the matrix calculation isperformed only on the transmission side is shown in FIG. 20. As shown inFIG. 20, a plurality of antennas are provided in a transmission station2001 located near a backbone network, and one antenna is provided inreception stations 2002 and 2003, located near a user network,respectively. The reception station 2001 and reception station 2003 arelocated far away from each other and, therefore, matrix calculationcannot be performed. On the other hand, the transmission station 2001can perform the matrix calculation. Thus, it is possible to apply theconfiguration in which the matrix calculation is performed only on thetransmission side to the configuration of FIG. 20. Such a concept in“one station to many stations” configuration may be applied to “manystations to one station” configuration to be described later as aconfiguration in which the matrix calculation is performed only on thereception side.

Third Example

As a third example of the present invention, a configuration example inwhich the unitary matrix calculation is performed only on the receptionside and local oscillators are provided independently for respectiveantennas on the transmission side will be described.

This third configuration has the following features: the feedbackinformation to be sent from the reception end to transmission end is notrequired; local oscillators may be provided independently for respectiveantennas on the transmission end; and exactly the same characteristicsas those of the SVD method can be shown.

[Singular Value Diagonal Matrix Λ^(1/2)]

In this example, the virtual orthogonal channels have the same value, sothat singular value diagonal matrix Λ^(1/2) is represented by thefollowing formula.

$\begin{matrix}{\Lambda^{1/2} = {\begin{bmatrix}\sqrt{\lambda_{1}} & 0 \\0 & \sqrt{\lambda_{2}}\end{bmatrix} = {\quad{\begin{bmatrix}\sqrt{2 + {2\cos \; \alpha}} & 0 \\0 & \sqrt{2 - {2\cos \; \alpha}}\end{bmatrix} = \begin{bmatrix}\sqrt{2} & 0 \\0 & \sqrt{2}\end{bmatrix}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 79} \right\rbrack\end{matrix}$

[Channel Matrix H]

In this example, the channel matrix H is represented by the followingformula.

$\begin{matrix}{\mspace{79mu} {{H = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {U \cdot \begin{bmatrix}\sqrt{2} & 0 \\0 & \sqrt{2}\end{bmatrix} \cdot \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}}}\mspace{79mu} {{where};}\mspace{79mu} {\Phi = {{{\Phi_{L} + \Phi_{A}}\therefore U} = {\begin{bmatrix}U_{11} & U_{12} \\U_{21} & U_{22}\end{bmatrix} = {{\begin{bmatrix}1 & {{- j} \cdot ^{j\Phi}} \\{- j} & {1 \cdot ^{j\Phi}}\end{bmatrix} \cdot \begin{bmatrix}{1\sqrt{2}} & 0 \\0 & {1\sqrt{2}}\end{bmatrix}} = {{\begin{bmatrix}{1/\sqrt{2}} & {{- j} \cdot {^{j\Phi}/\sqrt{2}}} \\{{- j}/\sqrt{2}} & {^{j\Phi}/\sqrt{2}}\end{bmatrix}\mspace{79mu}\therefore U^{H}} = \begin{bmatrix}{1/\sqrt{2}} & {j/\sqrt{2}} \\{j \cdot {^{- {j\Phi}}/\sqrt{2}}} & {^{j\Phi}/\sqrt{2}}\end{bmatrix}}}}}}\mspace{79mu} {{where};}\mspace{79mu} {\alpha = {{2{{\pi \left( \frac{d_{R}^{2}}{2R} \right)}/\gamma}} = {{\frac{\pi}{\gamma} \cdot \frac{d_{R}^{2}}{R}} = \frac{\pi}{2}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 80} \right\rbrack\end{matrix}$

A configuration obtained based on the above result is shown in FIG. 4.

As shown in FIG. 4, transmission side matrix calculation processingbased on the unitary matrix V is not performed at all, but all matrixcalculations are done on the reception side. As can be seen from[Numeral 80], in the case where the matrix calculation is performed onlyon the reception side, the matrix includes a variation between thechannels caused due to external factors such as a positional variation(modeled by Φ_(A) in FIG. 4) of the antennas highly sensitive to asubtle change of weather condition such as wind or surroundingtemperature. Thus, even when the displacement in the highly sensitiveantenna direction occurs, the unitary matrix acts so as to compensatefor the displacement.

Further, in this configuration, antenna interval must be widened in viewof a frequency to be used in the fixed point microwave communicationsystem and, correspondingly, local oscillators are installed near theantennas. That is, the point that the local oscillators are providedindependently for respective antennas on the transmission side is afeature of the third configuration.

In FIG. 4, transmission signal are added with pilot signals ofrespective antennas by a pilot signal generation section 401, frequencyconverted into signals of a radio frequency by a transmission sidefrequency conversion section 402 including local oscillators 404 and405, mixers 403 and 407, and then transmitted from a fixed antennasection 408 including a plurality of antennas as s₁ and s₂. The notationof the s₁ and s₂ based on equivalent baseband representation.

It should be noted here that the local oscillators 404 and 405 are usedindependently for respective antennas. Thus, carrier synchronization isnot achieved between carriers from the respective antennas, resulting ingeneration of phase noise Φ_(L). Reference numeral 406 is the modelingof the phase noise Φ_(L). The signals thus transmitted are received by areception side fixed antenna section 409 including a plurality ofantennas as r₁ and r₂. The notation of the r₁ and r₂ is based onequivalent baseband representation, and the frequency conversionprocessing into a signal of a baseband frequency is omitted here. Thereception signals r₁ and r₂ are processed by a reception side matrixcalculation processing section 410 based on the unitary matrix U,whereby signal separation/detection in MIMO is completed. It should benoted here that transmission side matrix calculation processing based onthe unitary matrix V is not performed at all, but all matrixcalculations are done on the reception side.

As can be seen from [Numeral 80], in the case where the matrixcalculation is performed only on the reception side, the matrix includesa variation between the channels caused due to external factors such asa positional variation (modeled by Φ_(A) in FIG. 4) of the antennashighly sensitive to a subtle change of weather condition such as wind orsurrounding temperature. Further, the matrix includes the phase noisedue to absence of synchronization between carriers. Thus, even when thedisplacement in the highly sensitive antenna direction or phase rotationbetween carriers occurs, the unitary matrix acts so as to compensate forthe displacement or phase rotation. The greatest merit of the thirdexample is that it is not necessary to send the feedback information forconstruction of the V matrix from the reception end to transmission end.The thick arrows of FIG. 4 denote virtual orthogonal channels in whichchannel qualities thereof are proportional to 2^(1/2) and 2^(1/2).

The antennas to be used are not particularly limited and may be aparabola antenna or a horn antenna.

As described above, even in the configuration in which the unitarymatrix calculation is not performed on the transmission end, theorthogonal channels can be formed. Further, even when the localoscillators are provided independently for respective antennas on thetransmission end, if phase difference Φ=Φ_(L)+Φ_(A) can be detected bypilot signals, the virtual orthogonal channels can be formed. Theorthogonal channels thus formed are not influenced by the phasedifference. Further, the feedback from the reception end to transmissionend is not required. Since the matrix used is the unitary matrix,exactly the same characteristics as those of the SVD method can beshown.

Fourth Example

As a fourth example of the present invention, a configuration example inwhich virtual orthogonal channels having the same width are formed, theunitary calculation is performed only on the reception side, and localoscillators are provided independently for respective antennas on boththe transmission and reception sides will be described.

This fourth configuration has the following features: the feedbackinformation to be sent from the reception end to transmission end is notrequired; local oscillators may be provided independently for respectiveantennas on both the transmission and reception sides; and exactly thesame characteristics as those of the SVD method can be shown. Further,analysis is made based on a fact that a significant phase rotation dueto movement in the antenna direction highly sensitive to a subtle changeof weather condition such as wind or surrounding temperature can betraced to the same modeling as a phase variation in the localoscillators provided for respective antennas both on the transmissionand reception sides. Note that the above theoretical analysisanalytically reveals that the above increase in channel capacity can beachieved even when such a displacement in the highly sensitive antennadirection occurs.

[Singular Value Diagonal Matrix Λ^(1/2)]

In this example, singular value diagonal matrix Λ^(1/2) is representedby the following formula.

$\begin{matrix}{\Lambda^{1/2} = {\quad{\begin{bmatrix}\sqrt{\lambda_{1}} & 0 \\0 & \sqrt{\lambda_{2}}\end{bmatrix} = {\quad{\begin{bmatrix}\sqrt{2 + {2\cos \; \alpha}} & 0 \\0 & \sqrt{2 - {2\cos \; \alpha}}\end{bmatrix} = {\quad\begin{bmatrix}\sqrt{2} & 0 \\0 & \sqrt{2}\end{bmatrix}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 81} \right\rbrack\end{matrix}$

[Channel Matrix H]

In this example, the channel matrix H is represented by the followingformula.

$\begin{matrix}{H = {\begin{bmatrix}1 & {{- j} \cdot ^{j\Phi}} \\{{- j} \cdot ^{j\varphi}} & {1 \cdot ^{j{({\Phi + \varphi})}}}\end{bmatrix} = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {U \cdot {\quad{{{\begin{bmatrix}\sqrt{2} & 0 \\0 & \sqrt{2}\end{bmatrix} \cdot \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}\mspace{79mu} {where}};\mspace{79mu} \left\{ {{\begin{matrix}{\Phi = {\Phi_{L} + \Phi_{A}}} \\{\varphi = {\varphi_{L} + \varphi_{A}}}\end{matrix}\therefore U} = {\begin{bmatrix}U_{11} & U_{12} \\U_{21} & U_{22}\end{bmatrix} = {\begin{bmatrix}1 & {{- j} \cdot ^{j\Phi}} \\{{- j} \cdot ^{j\Phi}} & {1 \cdot ^{j{({\Phi + \varphi})}}}\end{bmatrix} \cdot {\quad{\begin{bmatrix}{1/\sqrt{2}} & 0 \\0 & {1/\sqrt{2}}\end{bmatrix} = {\quad{{\begin{bmatrix}{1/\sqrt{2}} & {{- j} \cdot {^{- {j\Phi}}/\sqrt{2}}} \\{{- j} \cdot {^{- {j\varphi}}/\sqrt{2}}} & {^{j{({\Phi + \varphi})}}/\sqrt{2}}\end{bmatrix}\mspace{79mu}\therefore U^{H}} = {\quad{{\begin{bmatrix}{1/\sqrt{2}} & {j \cdot {^{- {j\varphi}}/\sqrt{2}}} \\{j \cdot {^{- {j\Phi}}/\sqrt{2}}} & {^{- {j{({\Phi + \varphi})}}}/\sqrt{2}}\end{bmatrix}\mspace{79mu} {where}};\mspace{79mu} {\alpha = {{2{{\pi\left( \frac{d_{R}^{2}}{2R} \right)}/\gamma}} = {{\frac{\pi}{\gamma} \cdot \frac{d_{R}^{2}}{R}} = \frac{\pi}{2}}}}}}}}}}}}} \right.}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 82} \right\rbrack\end{matrix}$

A configuration obtained based on the above result is shown in FIG. 5.

As shown in FIG. 5, transmission side matrix calculation processingbased on the unitary matrix V is not performed at all, but all matrixcalculations are done on the reception side. Even in the case where thematrix calculation is performed only on the reception side, the matrixincludes a variation between the channels caused due to external factorssuch as a positional variation (modeled by Φ_(A) and φ_(A) in FIG. 5) ofthe transmission and reception side antennas highly sensitive to asubtle change of weather condition such as wind or surroundingtemperature. Thus, even when the displacement in the highly sensitiveantenna direction occurs, the unitary matrix acts so as to compensatefor the displacement.

Further, in this configuration, antenna interval must be widened in viewof a frequency to be used in the fixed point microwave communicationsystem and, correspondingly, local oscillators are installed near theantennas. That is, the point that the local oscillators are providedindependently for respective antennas on both the transmission andreception sides is the biggest feature of the fourth configuration.Thus, even if the local oscillators are used independently forrespective antennas on both the transmission and reception sides, it ispossible to obtain characteristics equivalent to the SVD method byappropriately detecting the pilot signals.

In FIG. 5, transmission signal are added with pilot signals ofrespective antennas by a pilot signal generation section 501, frequencyconverted into signals of a radio frequency by a transmission sidefrequency conversion section 502 including local oscillators 504 and505, mixers 503 and 507, and then transmitted from a fixed antennasection 508 including a plurality of antennas as s₁ and s₂. The notationof the s₁ and s₂ is based on equivalent baseband representation.

It should be noted here that the local oscillators 504 and 505 are usedindependently for respective antennas. Thus, carrier synchronization isnot achieved between carriers from the respective antennas, resulting ingeneration of phase noise Φ_(L). Reference numeral 506 is the modelingof the phase noise Φ_(L).

The signals thus transmitted are received by a reception side fixedantenna section 509 including a plurality of antennas as r₁ and r₂. Thenotation of the r₁ and r₂ is based on equivalent basebandrepresentation. The reception signals r₁ and r₂ are frequency convertedinto signals of a baseband frequency by a reception side frequencyconversion section 510 including local oscillators 512 and 513, mixers511 and 515, passed through a pilot signal detection section 516, andprocessed by a reception side matrix calculation processing section 517based on the unitary matrix U, whereby signal separation/detection inMIMO is completed.

It should be noted here that the local oscillators 512 and 513 are usedindependently for respective antennas on the reception side. Thus, phasenoise Φ_(L) is generated due to absence of synchronization betweencarriers. Reference numeral 514 is the modeling of the phase noiseΦ_(L). The antennas to be used are not particularly limited and may be aparabola antenna or a horn antenna.

Since the pilot signals are generated before the processing performed bythe transmission side local oscillators and the pilot signals aredetected after the processing performed by the reception side localoscillators, the pilot signal detection section 516 can detectΦ=Φ_(L)+Φ_(A) and φ=φ_(L)+φ_(A) in [Numeral 82]. Thus, all matrixcalculations can be done only on the reception side with thetransmission side matrix calculation processing based on the unitarymatrix V omitted.

This is because that, as can be seen from [Numeral 82], the unitarymatrix acts so as to compensate for a variation between the channelscaused due to external factors such as a positional variation (modeledby Φ_(A) and φ_(A) in FIG. 5) of the antennas highly sensitive to asubtle change of weather condition such as wind or surroundingtemperature and phase noise Φ_(L) or φ_(L) caused due to absence ofsynchronization between carriers. The greatest merit of the fourthexample is that it is not necessary to send the feedback information forconstruction of the V matrix from the reception end to transmission end.The thick arrows of FIG. 5 denote virtual orthogonal channels in whichchannel qualities thereof are proportional to 2^(1/2) and 2^(1/2).

As described above, even in the configuration in which the unitarymatrix calculation is not performed on the transmission end, theorthogonal channels can be formed. Further, phase differenceΦ=Φ_(L)+Φ_(A) and phase noise φ=α_(L)+φ_(A) can be detected using thepilot signals. Thus, even in the case where the local oscillators areprovided independently for respective antennas on the transmission sideand/or reception end, the virtual orthogonal channels can be formed. Theorthogonal channels thus formed are not influenced by the phasedifference Φ or φ. The feedback from the reception end to thetransmission end is not required. Further, since the matrix used is theunitary matrix, exactly the same characteristics as those of the SVDmethod can be shown.

Fifth Example

As a fifth example of the present invention, a configuration example inwhich virtual orthogonal channels having different widths are formed,the matrix calculation is performed only on the reception side, andlocal oscillators are provided independently for respective antennas onboth the transmission and reception sides will be described.

This fifth example is an example in which virtual orthogonal channelshave different values. Also in this example, feedback information to besent from the reception end to transmission end is not required.Further, local oscillators may be provided independently for respectiveantennas on both the transmission and reception sides. In addition,analysis is made based on a fact that a significant phase rotation dueto movement in the antenna direction highly sensitive to a subtle changeof weather condition such as wind or surrounding temperature can betraced to the same modeling as a phase variation in the localoscillators provided for respective antennas both on the transmissionand reception sides. For flexibility, antenna distance is set based onantenna positions different from optimum antenna positions. Therefore,different characteristics from the SVD method are shown. Thecharacteristic analysis of this configuration will be described later.

[Singular Value Diagonal Matrix Λ^(1/2)]

In this example, the virtual orthogonal channels have different values,so that singular value diagonal matrix Λ^(1/2) is represented by thefollowing formula.

$\begin{matrix}{\Lambda^{1/2} = {\begin{bmatrix}\sqrt{\lambda_{1}} & 0 \\0 & \sqrt{\lambda_{2}}\end{bmatrix} = {\quad{\begin{bmatrix}\sqrt{2 + {2\cos \; \alpha}} & 0 \\0 & \sqrt{2 - {2\cos \; \alpha}}\end{bmatrix} = {\quad{\begin{bmatrix}{2{\cos \left( \frac{\alpha}{2} \right)}} & 0 \\0 & {2{\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix} = {\quad\begin{bmatrix}\left( {^{j\frac{\alpha}{2}} + ^{{- j}\frac{\alpha}{2}}} \right) & 0 \\0 & {- {j\left( {^{j\frac{\alpha}{2}} - ^{j\frac{\alpha}{2}}} \right)}}\end{bmatrix}}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 83} \right\rbrack\end{matrix}$

[Channel Matrix H]

In this example, the channel matrix H is represented by the followingformula.

$\begin{matrix}{{H = \begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\{^{- {j\alpha}} \cdot ^{j\varphi}} & {1 \cdot ^{j{({\Phi + \varphi})}}}\end{bmatrix}}{{where};}\left\{ \begin{matrix}{\Phi = {\Phi_{L} + \Phi_{A}}} \\{\varphi = {\varphi_{L} + \varphi_{A}}}\end{matrix} \right.} & \left\lbrack {{Numeral}\mspace{14mu} 84} \right\rbrack\end{matrix}$

Here, transmission side highly sensitive antenna displacement Φ_(A) isincluded in phase variation Φ_(L) in the transmission side localoscillators provided independently for respective antennas to obtain Φ,and reception side highly sensitive antenna displacement φ_(A) isincluded in phase variation φ_(L) in the reception side localoscillators provided independently for respective antennas to obtain.

$\begin{matrix}{H = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {\begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\{^{- {j\alpha}} \cdot ^{j\varphi}} & {1 \cdot ^{j{({\Phi + \varphi})}}}\end{bmatrix} = {U \cdot \begin{bmatrix}\left( {^{j\frac{\alpha}{2}} + ^{{- j}\frac{\alpha}{2}}} \right) & 0 \\0 & {- {j\left( {^{j\frac{\alpha}{2}} - ^{{- j}\frac{\alpha}{2\;}}} \right)}}\end{bmatrix} \cdot \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 85} \right\rbrack\end{matrix}$

Here, the above formula is satisfied and thus the following [Numeral 86]is satisfied.

$\begin{matrix}{U = {\begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\{^{- {j\alpha}} \cdot ^{j\varphi}} & {1 \cdot ^{j{({\Phi + \varphi})}}}\end{bmatrix} \cdot \begin{bmatrix}\left( {^{j\frac{\alpha}{2}} + ^{{- j}\frac{\alpha}{2}}} \right) & 0 \\0 & {- {j\left( {^{j\frac{\alpha}{2}} - ^{{- j}\frac{\alpha}{2}}} \right)}}\end{bmatrix}^{- 1}}} & \left\lbrack {{Numeral}\mspace{14mu} 86} \right\rbrack\end{matrix}$

Further, the following [Numeral 87] is satisfied and thus [Numeral 88]is satisfied.

$\begin{matrix}{\mspace{79mu} {{\frac{1}{\left( {^{j\frac{\alpha}{2}} + ^{{- j}\frac{\alpha}{2}}} \right)} = \frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}},\mspace{79mu} {\frac{1}{- {j\left( {^{j\frac{\alpha}{2}} - ^{{- j}\frac{\alpha}{2}}} \right)}} = \frac{1}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 87} \right\rbrack \\{U = {{\begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\{^{- {j\alpha}} \cdot ^{j\varphi}} & {1 \cdot ^{j{({\Phi + \varphi})}}}\end{bmatrix} \cdot \begin{bmatrix}\frac{1}{2{\cdot {\cos \left( \frac{\alpha}{2} \right)}}} & 0 \\0 & \frac{1}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix}} = {\quad\begin{bmatrix}\frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & \frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} \\\frac{^{- {j\alpha}} \cdot ^{j\varphi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & \frac{^{j{({\Phi + \varphi})}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix}}}} & \left\lbrack {{Numeral}\mspace{14mu} 88} \right\rbrack\end{matrix}$

However, the square norm of the vector is represented by the followingformula.

$\begin{matrix}{{\frac{1}{4 \cdot {\cos^{2}\left( \frac{\alpha}{2} \right)}} + \frac{1}{4 \cdot {\sin^{2}\left( \frac{\alpha}{2} \right)}}} = {\frac{4}{16 \cdot {\sin^{2}\left( \frac{\alpha}{2} \right)} \cdot {\cos^{2}\left( \frac{\alpha}{2} \right)}} = \frac{1}{2 \cdot {\sin^{2}(\alpha)}}}} & \left\lbrack {{Numeral}\mspace{14mu} 89} \right\rbrack\end{matrix}$

Thus, U is no longer a unitary matrix.

Therefore, in order to calculate the matrix U^(H), inverse matrixcalculation is required. As a trial, when the channel matrix H iscalculated using the obtained matrixes U, Λ^(1/2), and V^(H), thefollowing formula is satisfied.

$\begin{matrix}{\begin{matrix}{H = {U \cdot \Lambda^{1/2} \cdot V^{H}}} \\{= {\begin{bmatrix}\frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & \frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} \\\frac{^{- {j\alpha}} \cdot ^{j\varphi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & \frac{^{j{({\Phi + \varphi})}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix} \cdot}} \\{{\begin{bmatrix}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & 0 \\0 & {2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix} \cdot \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}} \\{= \begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\{^{- {j\alpha}} \cdot ^{j\varphi}} & {1 \cdot ^{j{({\Phi + \varphi})}}}\end{bmatrix}}\end{matrix}\quad} & \left\lbrack {{Numeral}\mspace{14mu} 90} \right\rbrack\end{matrix}$

As can be seen from the above, the channel matrix H is effected.

Next, inverse matrix of U⁻¹ of U is considered. A given matrix Arepresented by the following formula is assumed.

$\begin{matrix}{A = \begin{bmatrix}a_{11} & a_{12} \\a_{21} & a_{22}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 91} \right\rbrack\end{matrix}$

The inverse matrix A⁻¹ of the above matrix A is represented by thefollowing formula.

$\begin{matrix}{\mspace{79mu} {{A^{- 1} = {\frac{1}{{a_{11}a_{22}} - {a_{12}a_{21}}}\begin{bmatrix}a_{22} & {- a_{12}} \\{- a_{21}} & a_{11}\end{bmatrix}}}\left( {{\because{AA}^{- 1}} = {{{\frac{1}{{a_{11}a_{22}} - {a_{12}a_{21}}}\begin{bmatrix}a_{11} & a_{12} \\a_{21} & a_{22}\end{bmatrix}} \cdot \begin{bmatrix}a_{22} & {- a_{12}} \\{- a_{21}} & a_{11}\end{bmatrix}} = {\frac{1}{{a_{11}a_{22}} - {a_{12}a_{21}}}\begin{bmatrix}{{a_{11}a_{22}} - {a_{12}a_{21}}} & 0 \\0 & {{a_{11}a_{22}} - {a_{12}a_{21}}}\end{bmatrix}}}} \right)}} & \left\lbrack {{Numeral}\mspace{14mu} 92} \right\rbrack\end{matrix}$

Accordingly, the following formula is obtained.

$\begin{matrix}\begin{matrix}{U^{- 1} = \begin{bmatrix}\frac{1}{2{\cdot {\cos \left( \frac{\alpha}{2} \right)}}} & \frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} \\\frac{^{- {j\alpha}} \cdot ^{j\varphi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} & \frac{^{j{({\Phi + \varphi})}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix}^{- 1}} \\{= \frac{1}{{\frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}} \cdot \frac{^{j{({\Phi + \varphi})}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}} - {\frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} \cdot \frac{^{- {j\alpha}} \cdot ^{j\varphi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}}}} \\{\begin{bmatrix}\frac{^{j{({\Phi + \varphi})}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} & {- \frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}} \\{- \frac{^{- {j\alpha}} \cdot ^{j\varphi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}} & \frac{1}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}\end{bmatrix}} \\{= {\frac{2 \cdot \left( {2 \cdot {\sin \left( \frac{\alpha}{2} \right)} \cdot {\cos \left( \frac{\alpha}{2} \right)}} \right)}{1 - ^{{- {j2}} \cdot \alpha}}\begin{bmatrix}\frac{1}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}} & {- \frac{^{- {j\alpha}} \cdot ^{- {j\varphi}}}{2 \cdot {\sin \left( \frac{\alpha}{2} \right)}}} \\{- \frac{^{- {j\alpha}} \cdot ^{j\Phi}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}} & \frac{^{- {j{({\Phi + \varphi})}}}}{2 \cdot {\cos \left( \frac{\alpha}{2} \right)}}\end{bmatrix}}} \\{= {\frac{2}{1 - ^{{- {j2}} \cdot \alpha}}\begin{bmatrix}{\cos \left( \frac{\alpha}{2} \right)} & {{{- ^{- {j\alpha}}} \cdot ^{- {j\varphi}}}{\cos \left( \frac{\alpha}{2} \right)}} \\{{- ^{- {j\Phi}}}^{- {j\alpha}}{\sin \left( \frac{\alpha}{2} \right)}} & {^{- {j{({\Phi + \varphi})}}}{\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix}}} \\{= {\frac{2}{^{j\alpha} - ^{- {j\alpha}}}\begin{bmatrix}{^{j\alpha}{\cos \left( \frac{\alpha}{2} \right)}} & {{- ^{- {j\varphi}}}{\cos \left( \frac{\alpha}{2} \right)}} \\{{- ^{- {j\Phi}}}{\sin \left( \frac{\alpha}{2} \right)}} & {^{- {j{({\Phi + \varphi})}}}^{j\alpha}{\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix}}} \\{= {\frac{1}{j\; \sin \; \alpha}\begin{bmatrix}{^{j\alpha}{\cos \left( \frac{\alpha}{2} \right)}} & {{- ^{j\varphi}}{\cos \left( \frac{\alpha}{2} \right)}} \\{{- ^{- {j\Phi}}}{\sin \left( \frac{\alpha}{2} \right)}} & {^{- {j{({\Phi + \varphi})}}}^{j\alpha}{\sin \left( \frac{\alpha}{2} \right)}}\end{bmatrix}}} \\{= \begin{bmatrix}{{- {j}^{j\alpha}}\frac{\cos \left( {\alpha/2} \right)}{\sin \; \alpha}} & {{j}^{- {j\varphi}}\frac{\cos \left( {\alpha/2} \right)}{\sin \; \alpha}} \\{{j}^{- {j\Phi}}\frac{\sin \left( {\alpha/2} \right)}{\sin \; \alpha}} & {{- {j}^{- {j{({\Phi + \varphi})}}}}^{j\alpha}\frac{\sin \left( {\alpha/2} \right)}{\sin \; \alpha}}\end{bmatrix}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 93} \right\rbrack \\{\mspace{79mu} {{{where};}\mspace{79mu} {\alpha = {{2{{\pi \left( \frac{d_{R}^{2}}{2R} \right)}/\gamma}} = {\frac{\pi}{\gamma} \cdot \frac{d_{R}^{2}}{R}}}}}} & \;\end{matrix}$

A configuration obtained based on the above result is shown in FIG. 6.

Although a case of the virtual orthogonal channels having differentvalues has been described above, even if the local oscillators areprovided independently for respective antennas on both the transmissionand reception ends, it is possible to form the orthogonal channels byappropriately detecting the pilot signals. Since the matrix calculationis not performed on the transmission side, it is possible to eliminatethe feedback information to be sent from the reception end totransmission end and to deal with a rapid phase variation such astransmission end phase variation φ or reception end phase variation φ.

Thus, it is possible to form orthogonal channels having differentchannel quality regardless of whether the optimum position (R=5000 m andd_(T)=d_(R)=5 m) is achieved or not without the transmission side matrixcalculation processing. However, U^(H) is no longer a unitary matrix butbecomes an inverse matrix U⁻¹. Thus, characteristics are expected todegrade as compared to those of the SVD method. The difference in thecharacteristics between the SVD method and configuration of this examplewill be described later.

As shown in FIG. 6, transmission signals are added with pilot signalsorthogonal to each other for respective antennas by a pilot signalgeneration section 601. The orthogonal pilot signals used may be anorthogonal pattern obtained from the Hadamard matrix or may be a CAZACsequence. The transmission signals thus added with the pilot signals arefrequency converted into signals of a radio frequency by a transmissionside frequency conversion section 602 including local oscillators 604and 605, mixers 603 and 607, and then transmitted from a fixed antennasection 608 including a plurality of antennas as s₁ and s₂. The notationof the s₁ and s₂ is based on equivalent baseband representation.

It should be noted here that the local oscillators 604 and 605 are usedindependently for respective antennas. Thus, carrier synchronization isnot achieved between carriers from the respective antennas, resulting ingeneration of phase noise Φ_(L). Reference numeral 606 is the modelingof the phase noise Φ_(L). The signals thus transmitted are received by areception side fixed antenna section 609 including a plurality ofantennas as r₁ and r₂. The notation of the r₁ and r₂ is based onequivalent baseband representation. The reception signals r₁ and r₂ arefrequency converted into signals of a baseband frequency by a receptionside frequency conversion section 610 including local oscillators 612and 613, mixers 611 and 615, passed through a pilot signal detectionsection 616, and processed by a reception side matrix calculationprocessing section 617 based on the matrix U, whereby signalseparation/detection in MIMO is completed.

In the processing on the reception side, the local oscillators 612 and613 provided independently for respective antennas are used. Thus, phasenoise Φ_(L) is generated due to absence of carrier synchronizationbetween antennas. Reference numeral 614 is the modeling of the phasenoise Φ_(L). The antennas to be used are not particularly limited andmay be a parabola antenna or a horn antenna.

Since the orthogonal pilot signals are generated before the processingperformed by the transmission side local oscillators and the pilotsignals are detected after the processing performed by the receptionside local oscillators, the pilot signal detection section 616 candetect Φ=Φ_(L)+Φ_(A) and t=φ_(L)+Φ_(A) in [Numeral 93]. The orthogonalpilot signals used is an orthogonal pattern such as the Hadamardsequence or CAZAC sequence, so that the Φ and φ can be detected using asimple correlator (not shown). All matrix calculations can be done onlyon the reception side.

That is, as can be seen from [Numeral 93], the reception side matrixacts so as to compensate for a variation between the channels caused dueto external factors such as a positional variation (modeled by Φ_(A) andφ_(A) in FIG. 6) of the antennas highly sensitive to a subtle change ofweather condition such as wind or surrounding temperature and phasenoise Φ_(L) or φ_(L) caused due to absence of synchronization betweencarriers. The greatest merit of the fifth example is that it is notnecessary to send the feedback information for construction of the Vmatrix from the reception end to transmission end. The thick arrows ofFIG. 6 denote virtual orthogonal channels having different widths,unlike the fourth example. However, as described later, the virtualorthogonal channels in this configuration have the same channel quality.

Although a case where two antennas are used has been described, thepresent invention is not limited to this, but a configuration usingthree or more antennas is possible.

In the following, a case where three or more antennas are used will bedescribed. For simplification, only transmission/reception side-antennasare illustrated.

Sixth Example

A sixth example of the present invention shows a case where threeantennas are used and unitary matrix calculation is performed only onreception side.

[Singular Value Diagonal Matrix Λ^(1/2)]

In this example, singular value diagonal matrix Λ^(1/2) is representedby the following formula.

$\begin{matrix}{\Lambda^{1/2} = {\begin{bmatrix}\sqrt{\lambda_{1}} & 0 & 0 \\0 & \sqrt{\lambda_{2}} & 0 \\0 & 0 & \sqrt{\lambda_{3}}\end{bmatrix} = \begin{bmatrix}\sqrt{3} & 0 & 0 \\0 & \sqrt{3} & 0 \\0 & 0 & \sqrt{3}\end{bmatrix}}} & \left\lbrack {{Numeral}\mspace{14mu} 94} \right\rbrack\end{matrix}$

[Channel Matrix H]

In this example, the following [Numeral 95] is derived from FIG. 7, andchannel matrix H can be represented by [Numeral 96].

$\begin{matrix}{{\frac{\left( {n \cdot d} \right)^{2}}{R} = \frac{n^{2} \cdot \gamma}{3}}{{where};}{{n = 0},1,2}} & \left\lbrack {{Numeral}\mspace{14mu} 95} \right\rbrack \\{H = {\begin{bmatrix}1 & 0 & 0 \\0 & ^{{j\varphi}_{1}} & 0 \\0 & 0 & ^{{j\varphi}_{2}}\end{bmatrix} \cdot \begin{bmatrix}1 & ^{{- j}\frac{\pi}{3}} & ^{{- {j4}}\frac{\pi}{3}} \\^{{- j}\frac{\pi}{3}} & 1 & ^{{- j}\frac{\pi}{3}} \\^{{- {j4}}\frac{\pi}{3}} & ^{{- j}\frac{\pi}{3}} & 1\end{bmatrix} \cdot {\quad{{\begin{bmatrix}1 & 0 & 0 \\0 & ^{{j\Phi}_{1}} & 0 \\0 & 0 & ^{{j\Phi}_{2}}\end{bmatrix}{where}};\left\{ {\begin{matrix}{\Phi_{1} = {\Phi_{L_{1}} + \Phi_{A_{2}}}} \\{\Phi_{2} = {\Phi_{L_{2}} + \Phi_{A_{2}}}} \\{\varphi_{1} = {\varphi_{L_{1}} + \varphi_{A_{1}}}} \\{\varphi_{2} = {\varphi_{L_{2}} + \varphi_{A_{2}}}}\end{matrix} = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {{{U \cdot \begin{bmatrix}\sqrt{3} & 0 & 0 \\0 & \sqrt{3} & 0 \\0 & 0 & \sqrt{3}\end{bmatrix} \cdot \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}}\therefore U} = {\begin{bmatrix}U_{11} & U_{12} & U_{13} \\U_{21} & U_{22} & U_{23} \\U_{31} & U_{32} & U_{33}\end{bmatrix} = {\quad{{\quad\quad}{\quad{{{{\quad\quad}\begin{bmatrix}1 & {^{{- j}\frac{\pi}{3}} \cdot ^{{j\Phi}_{1}}} & {^{{- {j4}}\frac{\pi}{3}} \cdot ^{{j\Phi}_{2}}} \\{^{{- j}\frac{\pi}{3}} \cdot ^{{j\varphi}_{1}}} & {1 \cdot ^{j{({\varphi_{1} + \Phi_{1}})}}} & {^{{- j}\frac{\pi}{3}} \cdot ^{j{({\varphi_{1} + \Phi_{2}})}}} \\{^{{- {j4}}\frac{\pi}{3}} \cdot ^{{j\varphi}_{2}}} & {^{{- j}\frac{\pi}{3}} \cdot ^{j{({\varphi_{2} + \Phi_{1}})}}} & {1 \cdot ^{j{({\varphi_{2} + \Phi_{2}})}}}\end{bmatrix}} \cdot \begin{bmatrix}{1\sqrt{3}} & 0 & 0 \\0 & {1\sqrt{3}} & 0 \\0 & 0 & {1\sqrt{3}}\end{bmatrix}}{\quad{\quad{{\begin{bmatrix}\frac{1}{\sqrt{3}} & \frac{^{{- j}\frac{\pi}{3}} \cdot ^{{j\Phi}_{1}}}{\sqrt{3}} & \frac{^{{- {j4}}\frac{\pi}{3}} \cdot ^{{j\Phi}_{2}}}{\sqrt{3}} \\\frac{^{{- j}\frac{\pi}{3}} \cdot ^{{j\varphi}_{1}}}{\sqrt{3}} & \frac{1 \cdot ^{j{({\varphi_{1} + \Phi_{1}})}}}{\sqrt{3}} & \frac{^{{- j}\frac{\pi}{3}} \cdot ^{j{({\varphi_{1} + \Phi_{2}})}}}{\sqrt{3}} \\\frac{^{{- {j4}}\frac{\pi}{3}} \cdot ^{{j\varphi}_{2}}}{\sqrt{3}} & \frac{^{{- j}\frac{\pi}{3}} \cdot ^{j{({\varphi_{2} + \Phi_{1}})}}}{\sqrt{3}} & \frac{1 \cdot ^{j{({\varphi_{2} + \Phi_{2}})}}}{\sqrt{3}}\end{bmatrix}{\quad\quad}{where}};{\alpha = {{\frac{\pi}{\gamma} \cdot \frac{d^{2}}{R}} = \frac{\pi}{3}}}}}}}}}}}}}} \right.}}}} & \left\lbrack {{Numeral}\mspace{14mu} 96} \right\rbrack\end{matrix}$

Accordingly, the following formula is obtained.

$\begin{matrix}{{\therefore U^{H}} = \begin{bmatrix}\frac{1}{\sqrt{3}} & \frac{^{j\frac{\pi}{3}} \cdot ^{{- j}\; \varphi_{1}}}{\sqrt{3}} & \frac{^{j\; 4\frac{\pi}{3}} \cdot ^{{- j}\; \varphi_{2}}}{\sqrt{3}} \\\frac{^{j\frac{\pi}{3}} \cdot ^{{- j}\; \Phi_{1}}}{\sqrt{3}} & \frac{1 \cdot ^{- {j{({\varphi_{1} + \Phi_{1}})}}}}{\sqrt{3}} & \frac{^{j\frac{\pi}{3}} \cdot ^{{- j}\; {({\varphi_{2} + \Phi_{1}})}}}{\sqrt{3}} \\\frac{^{j\; 4\frac{\pi}{3}} \cdot ^{{- j}\; \Phi_{2}}}{\sqrt{3}} & \frac{^{j\frac{\pi}{3}} \cdot ^{{- j}\; {({\varphi_{1} + \Phi_{2}})}}}{\sqrt{3}} & \frac{1 \cdot ^{{- j}\; {({\varphi_{2} + \Phi_{1}})}}}{\sqrt{3}}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 97} \right\rbrack \\{\mspace{79mu} {{where};}} & \; \\{\mspace{79mu} \left\{ \begin{matrix}{\Phi_{1} = {\Phi_{L\; 1} + \Phi_{A\; 2}}} \\{\Phi_{2} = {\Phi_{L\; 2} + \Phi_{A\; 2}}} \\{\varphi_{1} = {\varphi_{L\; 1} + \varphi_{A\; 1}}} \\{\varphi_{2} = {\varphi_{L\; 2} + \varphi_{A\; 2}}}\end{matrix} \right.} & \;\end{matrix}$

Φ_(A) and φ_(A) in [Numeral 97] each represent a carrier phase rotationcaused due to a positional variation of the transmission/receptionside-antennas highly sensitive to a subtle change of weather conditionsuch as wind or surrounding temperature. Suffixes 1 and 2 represent apositional displacement of second and third antennas counting from theuppermost antennas. Further, antenna interval must be widened in view ofa frequency to be used in the fixed point microwave communication systemand, correspondingly, local oscillators are installed near the antennas.That is, the local oscillators are provided independently for respectiveantennas on both the transmission and reception sides. Accordingly,phase noise Φ_(L) or φ_(L) is caused due to absence of synchronizationbetween carriers. Suffixes 1 and 2 represent a positional displacementof second and third antennas counting from the uppermost antennas.

A significant phase rotation due to movement in the antenna directionhighly sensitive to a subtle change of weather condition such as wind orsurrounding temperature can be traced to the same modeling as a phasevariation in the local oscillators provided for respective antennas bothon the transmission and reception sides. Thus, the analysis based on[Numeral 97] reveals that Φ₁=φ_(L1)+Φ_(A1) and Φ₂=Φ_(L2)+Φ_(A2) aresatisfied in the transmission side second and third antennas countingfrom the uppermost antenna and φ₁=φ_(L1)+φ_(A1) and φ₂=φ_(L2)+φ_(A2) aresatisfied in the reception side second and third antennas counting fromthe uppermost antenna. That is, even in the configuration in which threeantennas are used, the virtual orthogonal channels can be formed by theunitary matrix calculation only on the reception side. The thick arrowsof FIG. 7 denote virtual orthogonal channels in which channel qualitiesthereof are proportional to 3^(1/2), 3^(1/2), and 3^(1/2).

Further, it is possible to obtain characteristics equivalent to the SVDmethod by appropriately detecting the phase differences using the pilotsignals. The channel capacity becomes three times higher than the totalpower delivered to all antennas.

Seventh Example

A seventh example of the present invention shows a case where fourantennas are used, unitary matrix calculation is performed only onreception side, and local oscillators on both transmission and receptionends are independently provided for respective antennas.

[Singular Value Diagonal Matrix Λ^(1/2)]

In this example, singular value diagonal matrix Λ^(1/2) is representedby the following formula.

$\begin{matrix}{\Lambda^{1/2} = {\begin{bmatrix}\sqrt{\lambda_{1}} & 0 & 0 & 0 \\0 & \sqrt{\lambda_{2}} & 0 & 0 \\0 & 0 & \sqrt{\lambda_{3}} & 0 \\0 & 0 & 0 & \sqrt{\lambda_{4}}\end{bmatrix} = {\quad\begin{bmatrix}\sqrt{4} & 0 & 0 & 0 \\0 & \sqrt{4} & 0 & 0 \\0 & 0 & \sqrt{4} & 0 \\0 & 0 & 0 & \sqrt{4}\end{bmatrix}}}} & \left\lbrack {{Numeral}\mspace{14mu} 98} \right\rbrack\end{matrix}$

[Channel Matrix H]

In this example, the following [Numeral 99] is derived from FIG. 8,

$\begin{matrix}{{{\frac{\left( {n \cdot d} \right)^{2}}{R} = {\frac{n^{2} \cdot \gamma}{4}\mspace{14mu} {where}}};{n = 0}},1,2,3} & \left\lbrack {{Numeral}\mspace{14mu} 99} \right\rbrack\end{matrix}$

and channel matrix H can be represented by the following [Numeral 100].

$\begin{matrix}\begin{matrix}{H = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & ^{j\; \varphi_{1}} & 0 & 0 \\0 & 0 & ^{j\; \varphi_{2}} & 0 \\0 & 0 & 0 & ^{j\; \varphi_{3}}\end{bmatrix} \cdot \begin{bmatrix}1 & ^{{- j}\frac{\pi}{4}} & ^{{- j}\frac{4\; \pi}{4}} & ^{{- j}\frac{9\; \pi}{4}} \\^{{- j}\frac{\pi}{4}} & 1 & ^{{- j}\frac{\pi}{4}} & ^{{- j}\frac{4\; \pi}{4}} \\^{{- j}\frac{4\; \pi}{4}} & ^{{- j}\frac{\pi}{4}} & 1 & ^{{- j}\frac{\pi}{4}} \\^{{- j}\frac{9\; \pi}{4}} & ^{{- j}\frac{4\; \pi}{4}} & ^{{- j}\frac{\pi}{4}} & 1\end{bmatrix} \cdot \begin{bmatrix}1 & 0 & 0 & 0 \\0 & ^{j\; \varphi_{1}} & 0 & 0 \\0 & 0 & ^{j\; \varphi_{2}} & 0 \\0 & 0 & 0 & ^{j\; \varphi_{3}}\end{bmatrix}}} \\ \\{= {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {U \cdot {\quad{\begin{bmatrix}\sqrt{4} & 0 & 0 & 0 \\0 & \sqrt{4} & 0 & 0 \\0 & 0 & \sqrt{4} & 0 \\0 & 0 & 0 & \sqrt{4}\end{bmatrix} \cdot \begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}}}}}} \\{{{where};\; \left\{ \begin{matrix}{\Phi_{1} = {\Phi_{L\; 1} + \Phi_{A\; 2}}} \\{\Phi_{2} = {\Phi_{L\; 2} + \Phi_{A\; 2}}} \\{\Phi_{3} = {\Phi_{L\; 3} + \Phi_{A\; 3}}} \\{\varphi_{1} = {\varphi_{L\; 1} + \varphi_{A\; 1}}} \\{\varphi_{2} = {\varphi_{L\; 2} + \varphi_{A\; 2}}} \\{\varphi_{2} = {\varphi_{L\; 3} + \varphi_{A\; 3}}}\end{matrix} \right.}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 100} \right\rbrack \\\begin{matrix}{{\therefore U} = {\begin{bmatrix}1 & {^{{- j}\frac{\pi}{4}} \cdot ^{j\; \Phi_{1}}} & {^{{- j}\frac{4\; \pi}{4}} \cdot ^{j\; \Phi_{2}}} & {^{{- j}\frac{9\; \pi}{4}} \cdot ^{j\; \Phi_{3}}} \\{^{{- j}\frac{\pi}{4}} \cdot ^{j\; \varphi_{1}}} & {1 \cdot ^{j{({\varphi_{1} + \Phi_{1}})}}} & {^{{- j}\frac{\pi}{4}} \cdot ^{j\; {({\varphi_{1} + \Phi_{2}})}}} & {^{{- j}\frac{4\; \pi}{4}} \cdot ^{j\; {({\varphi_{1} + \Phi_{3}})}}} \\{^{{- j}\frac{4\; \pi}{4}} \cdot ^{j\; \varphi_{2}}} & {^{{- j}\frac{\pi}{4}} \cdot ^{j\; {({\varphi_{2} + \Phi_{1}})}}} & {1 \cdot ^{j{({\varphi_{2} + \Phi_{2}})}}} & {^{{- j}\frac{\pi}{4}} \cdot ^{j{({\varphi_{2} + \Phi_{3}})}}} \\{^{{- j}\frac{9\; \pi}{4}} \cdot ^{j\; \varphi_{3}}} & {^{{- j}\frac{4\; \pi}{4}} \cdot ^{j\; {({\varphi_{3} + \Phi_{1}})}}} & {^{{- j}\frac{\pi}{4}} \cdot ^{j\; {({\varphi_{3} + \Phi_{2}})}}} & {1 \cdot ^{j{({\varphi_{3} + \Phi_{3}})}}}\end{bmatrix} \cdot}} \\{\begin{bmatrix}{1/\sqrt{4}} & 0 & 0 & 0 \\0 & {1/\sqrt{4}} & 0 & 0 \\0 & 0 & {1/\sqrt{4}} & 0 \\0 & 0 & 0 & {1/\sqrt{4}}\end{bmatrix}} \\{= \begin{bmatrix}\frac{1}{\sqrt{4}} & \frac{^{{- j}\frac{\pi}{4}} \cdot ^{j\; \Phi_{1}}}{\sqrt{4}} & \frac{^{{- j}\frac{4\; \pi}{4}} \cdot ^{j\; \Phi_{2}}}{\sqrt{4}} & \frac{^{{- j}\frac{9\; \pi}{4}} \cdot ^{j\; \Phi_{3}}}{\sqrt{4}} \\\frac{^{{- j}\frac{\pi}{4}} \cdot ^{j\; \varphi_{1}}}{\sqrt{4}} & \frac{1 \cdot ^{j{({\varphi_{1} + \Phi_{1}})}}}{\sqrt{4}} & \frac{^{{- j}\frac{\pi}{4}} \cdot ^{j{({\varphi_{1} + \Phi_{2}})}}}{\sqrt{4}} & \frac{^{{- j}\frac{4\; \pi}{4}} \cdot ^{j{({\varphi_{1} + \Phi_{3}})}}}{\sqrt{4}} \\\frac{^{{- j}\frac{4\; \pi}{4}} \cdot ^{j\; \varphi_{2}}}{\sqrt{4}} & \frac{^{{- j}\frac{\pi}{4}} \cdot ^{j{({\varphi_{2} + \Phi_{1}})}}}{\sqrt{4}} & \frac{1 \cdot ^{j{({\varphi_{2} + \Phi_{2}})}}}{\sqrt{4}} & \frac{^{{- j}\frac{\pi}{4}} \cdot ^{j{({\varphi_{2} + \Phi_{3}})}}}{\sqrt{4}} \\\frac{^{{- j}\frac{9\; \pi}{4}} \cdot ^{j\; \varphi_{3}}}{\sqrt{4}} & \frac{^{{- j}\frac{4\; \pi}{4}} \cdot ^{j{({\varphi_{3} + \Phi_{1}})}}}{\sqrt{4}} & \frac{^{{- j}\frac{\pi}{4}} \cdot ^{j{({\varphi_{3} + \Phi_{2}})}}}{\sqrt{4}} & \frac{1 \cdot ^{j{({\varphi_{3} + \Phi_{3}})}}}{\sqrt{4}}\end{bmatrix}} \\{{{where};{\alpha = {{\frac{\pi}{\gamma} \cdot \frac{d^{2}}{R}} = \frac{\pi}{4}}}}}\end{matrix} & \;\end{matrix}$

Accordingly, the following formula is obtained.

$\mspace{625mu} {{\left\lbrack {{Numeral}\mspace{14mu} 101} \right\rbrack \therefore U^{H}} = {\quad{{\begin{bmatrix}\frac{1}{\sqrt{4}} & \frac{^{j\frac{\pi}{4}} \cdot ^{{- j}\; \varphi_{1}}}{\sqrt{4}} & \frac{^{j\frac{4\; \pi}{4}} \cdot ^{{- j}\; \varphi_{2}}}{\sqrt{4}} & \frac{^{j\frac{9\; \pi}{4}} \cdot ^{{- j}\; \varphi_{3}}}{\sqrt{4}} \\\frac{^{j\frac{\pi}{4}} \cdot ^{{- j}\; \Phi_{1}}}{\sqrt{4}} & \frac{1 \cdot ^{- {j{({\varphi_{1} + \Phi_{1}})}}}}{\sqrt{4}} & \frac{^{j\frac{\pi}{4}} \cdot ^{- {j{({\varphi_{2} + \Phi_{1}})}}}}{\sqrt{4}} & \frac{^{j\frac{4\; \pi}{4}} \cdot ^{- {j{({\varphi_{3} + \Phi_{1}})}}}}{\sqrt{4}} \\\frac{^{j\frac{4\; \pi}{4}} \cdot ^{{- j}\; \Phi_{2}}}{\sqrt{4}} & \frac{^{j\frac{\pi}{4}} \cdot ^{- {j{({\varphi_{1} + \Phi_{2}})}}}}{\sqrt{4}} & \frac{1 \cdot ^{- {j{({\varphi_{2} + \Phi_{2}})}}}}{\sqrt{4}} & \frac{^{j\frac{\pi}{4}} \cdot ^{- {j{({\varphi_{3} + \Phi_{2}})}}}}{\sqrt{4}} \\\frac{^{j\frac{9\; \pi}{4}} \cdot ^{{- j}\; \Phi_{3}}}{\sqrt{4}} & \frac{^{j\frac{4\; \pi}{4}} \cdot ^{- {j{({\varphi_{1} + \Phi_{3}})}}}}{\sqrt{4}} & \frac{^{j\frac{\pi}{4}} \cdot ^{- {j{({\varphi_{2} + \Phi_{3}})}}}}{\sqrt{4}} & \frac{1 \cdot ^{- {j{({\varphi_{3} + \Phi_{3}})}}}}{\sqrt{4}}\end{bmatrix}\mspace{20mu} {where}};\left\{ \begin{matrix}{\Phi_{1} = {\Phi_{L_{1}} + \Phi_{A_{2}}}} \\{\Phi_{2} = {\Phi_{L_{2}} + \Phi_{A_{2}}}} \\{\Phi_{3} = {\Phi_{L_{3}} + \Phi_{A_{3}}}} \\{\varphi_{1} = {\varphi_{L_{1}} + \varphi_{A_{1}}}} \\{\varphi_{2} = {\varphi_{L_{2}} + \varphi_{A_{2}}}} \\{\varphi_{2} = {\varphi_{L_{3}} + \varphi_{A_{3}}}}\end{matrix} \right.}}}$

Φ_(A) and φ_(A) in [Numeral 101] each represent a carrier phase rotationcaused due to a positional variation of the transmission/receptionside-antennas highly sensitive to a subtle change of weather conditionsuch as wind or surrounding temperature. Suffixes 1, 2, and 3 representa positional displacement of second, third, and fourth antennas countingfrom the uppermost antennas. Antenna interval must be widened in view ofa frequency to be used in the fixed point microwave communication systemand, correspondingly, local oscillators are installed near the antennas.That is, the local oscillators are provided independently for respectiveantennas on both the transmission and reception sides. Accordingly,phase noise φ_(L) or φ_(L) is caused due to absence of synchronizationbetween carriers. Suffixes 1, 2, and 3 represent a positionaldisplacement of local oscillators of second, third, and fourth antennascounting from the uppermost antennas.

A significant phase rotation due to movement in the antenna directionhighly sensitive to a subtle change of weather condition such as wind orsurrounding temperature can be traced to the same modeling as a phaserotation in the local oscillators provided for respective antennas bothon the transmission and reception sides. Thus, the analysis based on[Numeral 101] reveals that Φ₁=Φ_(L1)+Φ_(A1), Φ₂=Φ_(L2)+Φ_(A2), andΦ₃=Φ_(L3)+Φ_(A3) are satisfied in the transmission side second, third,and fourth antennas counting from the uppermost antenna andφ₁=φ_(L1)+φ_(A1), φ₂=φ_(L2)+φ_(A2), and φ₃=φ_(L3)+φ_(A3) are satisfiedin the reception side second, third, and fourth antennas counting fromthe uppermost antenna. That is, even in the configuration in which fourantennas are used, the virtual orthogonal channels can be formed by theunitary matrix calculation only on the reception side. The thick arrowsof FIG. 8 denote virtual orthogonal channels in which channel qualitiesthereof are proportional to 4^(1/2), 4^(1/2), 4^(1/2), and 4^(1/2).

Further, it is possible to obtain characteristics equivalent to the SVDmethod by appropriately detecting the phase variations using the pilotsignals. The channel capacity becomes four times higher than the totalpower delivered to all antennas.

In the following, a case where an arbitrary number N of antennas areused will be described for respective cases where matrix calculation isperformed only on the transmission side, where only on the receptionside, and where both on the transmission and reception sides.

In this example, a configuration (general solution) using an arbitrarynumber N of antennas is considered.

[Singular Value Diagonal Matrix Λ^(1/2)]

In this example, singular value diagonal matrix Λ^(1/2) is representedby the following formula.

$\begin{matrix}{\Lambda^{1/2} = {\begin{bmatrix}\sqrt{\lambda_{1}} & 0 & \ldots & 0 \\0 & \sqrt{\lambda_{2}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \sqrt{\lambda_{N}}\end{bmatrix} = {\quad\begin{bmatrix}\sqrt{N} & 0 & \ldots & 0 \\0 & \sqrt{N} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \sqrt{N}\end{bmatrix}}}} & \left\lbrack {{Numeral}\mspace{14mu} 102} \right\rbrack\end{matrix}$

Based on the following [Numeral 103], an ideal line-of-sight channelmatrix where there is no phase rotation on both the transmission andreception sides is represented by [Numeral 104].

$\begin{matrix}{{{\frac{\left( {n \cdot d} \right)^{2}}{R} = {\frac{n^{2} \cdot \gamma}{N}\mspace{14mu} {where}}};{n = 0}},1,2,3,\ldots \mspace{14mu},{N - 1}} & \left\lbrack {{Numeral}\mspace{14mu} 103} \right\rbrack \\{H_{0} = \begin{bmatrix}1 & ^{{- j}\frac{\pi}{N}} & \ldots & ^{{- j}\frac{{({N - 1})}^{2}\pi}{N}} \\^{{- j}\frac{\pi}{N}} & 1 & \ddots & ^{{- j}\frac{{({N - 2})}^{2}\pi}{N}} \\\vdots & \ddots & \ddots & \vdots \\^{{- j}\frac{{({N - 1})}^{2}\pi}{N}} & ^{{- j}\frac{{({N - 2})}^{2}\pi}{N}} & \ldots & 1\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 104} \right\rbrack\end{matrix}$

Further, a transmission side phase rotation matrix T is defined as thefollowing formula.

$\begin{matrix}{T = \begin{bmatrix}1 & 0 & \ldots & 0 \\0 & ^{j\; \Phi_{1}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & ^{j\; \Phi_{N - 1}}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 105} \right\rbrack\end{matrix}$

Similarly, a reception side phase rotation matrix W is defined as theright formula.

$\begin{matrix}{W = \begin{bmatrix}1 & 0 & \ldots & 0 \\0 & ^{j\; \varphi_{1}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & ^{j\; \varphi_{N - 1}}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 106} \right\rbrack\end{matrix}$

Here, the following [Numeral 107] and [Numeral 108] are both satisfied.

$\begin{matrix}\left\{ \begin{matrix}{\varphi_{1} = {\varphi_{L_{1}} + \varphi_{A_{1}}}} \\\vdots \\{\varphi_{N - 1} = {\varphi_{L_{N - 1}} + \varphi_{A_{N - 1}}}}\end{matrix} \right. & \left\lbrack {{Numeral}\mspace{14mu} 107} \right\rbrack \\\left\{ \begin{matrix}{\Phi_{1} = {\Phi_{L_{1}} + \Phi_{A_{1}}}} \\\vdots \\{\Phi_{N - 1} = {\Phi_{L_{N - 1}} + \Phi_{A_{N - 1}}}}\end{matrix} \right. & \left\lbrack {{Numeral}\mspace{14mu} 108} \right\rbrack\end{matrix}$

Φ_(A) and φ_(A) each represent a carrier phase rotation caused due to apositional variation of the transmission/reception side-antennas highlysensitive to a subtle change of weather condition such as wind orsurrounding temperature. Φ_(L) or Φ_(L) represents a phase variationcaused due to absence of synchronization between carriers. Each Suffixrepresents the location corresponding to each antenna with respect tothe uppermost antennas.

Thus, an actual line-of-sight channel matrix where a phase rotation ispresent on both the transmission and reception sides is represented bythe following formula.

$\begin{matrix}{H = {{W \cdot H_{0} \cdot T} = {\begin{bmatrix}1 & 0 & \ldots & 0 \\0 & ^{j\; \varphi_{1}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & ^{j\; \varphi_{N - 1}}\end{bmatrix} \cdot {\quad{\begin{bmatrix}1 & ^{{- j}\frac{\pi}{N}} & \ldots & ^{{- j}\frac{{({N - 1})}^{2}\pi}{N}} \\^{{- j}\frac{\pi}{N}} & 1 & \ddots & ^{{- j}\frac{{({N - 2})}^{2}\pi}{N}} \\\vdots & \ddots & \ddots & \vdots \\^{{- j}\frac{{({N - 1})}^{2}\pi}{N}} & ^{{- j}\frac{{({N - 2})}^{2}\pi}{N}} & \ldots & 1\end{bmatrix} \cdot {\quad\begin{bmatrix}1 & 0 & \ldots & 0 \\0 & ^{j\; \Phi_{1}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & ^{j\; \Phi_{N - 1}}\end{bmatrix}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 109} \right\rbrack\end{matrix}$

(Case where Unitary Matrix Calculation is Performed Only on ReceptionSide)

In this case, the following formula is satisfied.

$\begin{matrix}{H = {{W \cdot H_{0} \cdot T} = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {U \cdot {\quad{\begin{bmatrix}\sqrt{N} & 0 & \ldots & 0 \\0 & \sqrt{N} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \sqrt{N}\end{bmatrix} \cdot \begin{bmatrix}1 & 0 & \ldots & 0 \\0 & 1 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 1\end{bmatrix}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 110} \right\rbrack\end{matrix}$

Accordingly, the following formula is satisfied.

$\begin{matrix}{U = {\frac{1}{\sqrt{N}} \cdot W \cdot H_{0} \cdot T}} & \left\lbrack {{Numeral}\mspace{14mu} 111} \right\rbrack\end{matrix}$

Thus, the following formula is obtained.

$\begin{matrix}\begin{matrix}{U^{H} = {\frac{1}{\sqrt{N}} \cdot T^{H} \cdot H_{0}^{H} \cdot W^{H}}} \\{= {\frac{1}{\sqrt{N}} \cdot {\quad{\begin{bmatrix}1 & 0 & \ldots & 0 \\0 & ^{{- j}\; \Phi_{1}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & ^{{- j}\; \Phi_{N - 1}}\end{bmatrix} \cdot}}}} \\{{\begin{bmatrix}1 & ^{j\frac{\pi}{N}} & \ldots & ^{j\frac{{({N - 1})}^{2}\pi}{N}} \\^{j\frac{\pi}{N}} & 1 & \ddots & ^{j\frac{{({N - 2})}^{2}\pi}{N}} \\\vdots & \ddots & \ddots & \vdots \\^{j\frac{{({N - 1})}^{2}\pi}{N}} & ^{j\frac{{({N - 2})}^{2}\pi}{N}} & \ldots & 1\end{bmatrix} \cdot}} \\{\begin{bmatrix}1 & 0 & \ldots & 0 \\0 & ^{{- j}\; \varphi_{1}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & ^{{- j}\; \varphi_{N - 1}}\end{bmatrix}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 112} \right\rbrack\end{matrix}$

That is, even in the configuration in which arbitrary number N ofantennas are used, the virtual orthogonal channels can be formed by thematrix calculation only on the reception side even in the case where thelocal oscillators are provided independently for respective antennas andwhere a displacement in the highly sensitive antenna direction occurs.

Incidentally, it is assumed that the following formula is satisfied.

$\begin{matrix}{{U^{H} \cdot U} = {{\frac{1}{\sqrt{N}} \cdot T^{H} \cdot H_{0}^{H} \cdot W^{H} \cdot \frac{1}{\sqrt{N}} \cdot W \cdot H_{0} \cdot T} = {\frac{1}{N}{T^{H} \cdot H_{0}^{H} \cdot H_{0} \cdot T}}}} & \left\lbrack {{Numeral}\mspace{14mu} 113} \right\rbrack\end{matrix}$

Here, the following formula is satisfied.

$\begin{matrix}{{H_{o}^{H} \cdot H_{o}} = {\begin{bmatrix}1 & ^{j\; \frac{\pi}{N}} & \cdots & ^{j\; \frac{{({N - 1})}^{2}\pi}{N}} \\^{j\; \frac{x}{N}} & 1 & \ddots & ^{j\; \frac{{({N - 2})}^{2}\pi}{N}} \\\vdots & \ddots & \ddots & \vdots \\^{j\; \frac{{({N - 1})}^{2}\pi}{N}} & ^{j\; \frac{{({N - 2})}^{2}\pi}{N}} & \cdots & 1\end{bmatrix} \cdot {\quad{\begin{bmatrix}1 & ^{{- j}\; \frac{\pi}{N}} & \cdots & ^{{- j}\; \frac{{({N - 1})}^{2}\pi}{N}} \\^{{- j}\; \frac{\pi}{N}} & 1 & \ddots & ^{{- j}\; \frac{{({N - 2})}^{2}\pi}{N}} \\\vdots & \ddots & \ddots & \vdots \\^{{- j}\; \frac{{({N - 1})}^{2}\pi}{N}} & ^{{- j}\; \frac{{({N - 2})}^{2}\pi}{N}} & \cdots & 1\end{bmatrix} = {N \cdot I}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 114} \right\rbrack\end{matrix}$

When N is an even number, an arbitrary column vector or arbitrary rowvector is a vector obtained by cyclic shifting Chu sequence, and theautocorrelation values thereof (E[a·a*]) are orthogonal to each other.When N is an odd number, cyclic shift does not appear. However, it canbe understood from the following description that the orthogonalrelationship has been established.

(Case where Unitary Matrix Calculation is Performed Only on TransmissionSide)

In this case, the following formula is satisfied.

$\begin{matrix}{H = {{W \cdot H_{o} \cdot T} = {{U \cdot \Lambda^{1/2} \cdot V^{H}} = {\begin{bmatrix}1 & 0 & \cdots & 0 \\0 & 1 & \cdots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \cdots & 1\end{bmatrix} \cdot {\quad{\begin{bmatrix}\sqrt{N} & 0 & \cdots & 0 \\0 & \sqrt{N} & \cdots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \cdots & \sqrt{N}\end{bmatrix} \cdot V^{H}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 115} \right\rbrack\end{matrix}$

Accordingly, the following formula is satisfied.

$\begin{matrix}{V^{H} = {\frac{1}{\sqrt{N}} \cdot W \cdot H_{o} \cdot T}} & \left\lbrack {{Numeral}\mspace{14mu} 116} \right\rbrack\end{matrix}$

Thus, the following formula is obtained.

$\begin{matrix}{V = {{\frac{1}{\sqrt{N}} \cdot T^{H} \cdot H_{o}^{H} \cdot W^{H}} = {\frac{1}{\sqrt{N}} \cdot \begin{bmatrix}1 & 0 & \cdots & 0 \\0 & ^{- {j\Phi}_{1}} & \cdots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \cdots & ^{- {j\Phi}_{N - 1}}\end{bmatrix} \cdot {\quad{\begin{bmatrix}1 & ^{j\; \frac{\pi}{N}} & \cdots & ^{j\frac{{({N - 1})}^{2}\pi}{4}} \\^{j\; \frac{\pi}{N}} & 1 & \ddots & ^{j\frac{{({N - 2})}^{2}\pi}{4}} \\\vdots & \ddots & \ddots & \vdots \\^{j\frac{{({N - 1})}^{2}\pi}{4}} & ^{j\frac{{({N - 2})}^{2}\pi}{4}} & \cdots & 1\end{bmatrix} \cdot {\quad\begin{bmatrix}1 & 0 & \cdots & 0 \\0 & ^{- {j\varphi}_{1}} & \cdots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \cdots & ^{- {j\varphi}_{N - 1}}\end{bmatrix}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 117} \right\rbrack\end{matrix}$

That is, even in the configuration in which arbitrary number N ofantennas are used, the virtual orthogonal channels can be formed by thematrix calculation V only on the transmission side even in the casewhere the local oscillators are provided independently for respectiveantennas and where a displacement in the highly sensitive antennadirection occurs.

(Case where Unitary Matrix Calculation is Performed Both on Transmissionand Reception Sides)

[Singular Value Diagonal Matrix Λ^(1/2)]

In this case, singular value diagonal matrix Λ^(1/2) is represented bythe following formula.

$\begin{matrix}{\Lambda^{1/2} = {\begin{bmatrix}\sqrt{\lambda_{1}} & 0 & \cdots & 0 \\0 & \sqrt{\lambda_{2}} & \cdots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \cdots & \sqrt{\lambda_{N}}\end{bmatrix} = {\quad\begin{bmatrix}\sqrt{N} & 0 & \cdots & 0 \\0 & \sqrt{N} & \cdots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \cdots & \sqrt{N}\end{bmatrix}}}} & \left\lbrack {{Numeral}\mspace{14mu} 118} \right\rbrack\end{matrix}$

Accordingly, the following formula is obtained.

H=W·H ₀ ·T=U·Λ ^(1/2) ·V ^(H) =√{square root over (N)}·U·V^(H)  [Numeral 119]

When an arbitrary unitary matrix is used as V, the following formula isobtained.

$\begin{matrix}{U = {\frac{1}{\sqrt{N}} \cdot W \cdot H_{o} \cdot T \cdot V}} & \left\lbrack {{Numeral}\mspace{14mu} 120} \right\rbrack\end{matrix}$

Incidentally, the following formula is satisfied.

$\begin{matrix}{{U^{H} \cdot U} = {{\frac{1}{\sqrt{N}} \cdot V^{H} \cdot T^{H} \cdot H_{o}^{H} \cdot W^{H} \cdot \frac{1}{\sqrt{N}} \cdot W \cdot H_{o} \cdot T \cdot V} = {{\frac{1}{\sqrt{N}} \cdot N \cdot I} = I}}} & \left\lbrack {{Numeral}\mspace{14mu} 121} \right\rbrack\end{matrix}$

Thus, even when an arbitrary unitary matrix is used as V, U becomes aunitary matrix.

Accordingly, the following formula is obtained.

$\begin{matrix}{U^{H} = {{\frac{1}{\sqrt{N}} \cdot V^{H} \cdot T^{H} \cdot H_{o}^{H} \cdot W^{H}} = {\frac{V^{H}}{\sqrt{N}} \cdot \begin{bmatrix}1 & 0 & \cdots & 0 \\0 & ^{- {j\Phi}_{1}} & \cdots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \cdots & ^{- {j\Phi}_{N - 1}}\end{bmatrix} \cdot {\quad{\begin{bmatrix}1 & ^{j\; \frac{\pi}{N}} & \cdots & ^{j\frac{{({N - 1})}^{2}\pi}{N}} \\^{j\; \frac{\pi}{N}} & 1 & \ddots & ^{j\frac{{({N - 2})}^{2}\pi}{N}} \\\vdots & \ddots & \ddots & \vdots \\^{j\frac{{({N - 1})}^{2}\pi}{N}} & ^{j\frac{{({N - 2})}^{2}\pi}{N}} & \cdots & 1\end{bmatrix} \cdot {\quad\begin{bmatrix}1 & 0 & \cdots & 0 \\0 & ^{- {j\varphi}_{1}} & \cdots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \cdots & ^{- {j\varphi}_{N - 1}}\end{bmatrix}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 122} \right\rbrack\end{matrix}$

That is, even when an arbitrary number N of antennas are used in theconfiguration in which unitary matrix calculation is performed both onthe transmission and reception sides, the virtual orthogonal channelscan be formed by the unitary matrix calculation only on the receptionside even in the case where the local oscillators are providedindependently for respective antennas and where a displacement in thehighly sensitive antenna direction occurs.

At this time, a fixed transmission matrix V may be any one as long as itis a unitary matrix, and a reception side unitary matrix calculation isrepresented by the following formula to act so as to compensate for avariation caused by the local oscillators or due to antennadisplacement.

$\begin{matrix}{U^{H} = {\frac{V^{H}}{\sqrt{N}} \cdot T^{H} \cdot H_{o}^{H} \cdot W^{H}}} & \left\lbrack {{Numeral}\mspace{14mu} 123} \right\rbrack\end{matrix}$

As a simple example, the above formula is applied to a configuration inwhich two antennas are used.

As a fixed arbitrary transmission matrix, a matrix represented by thefollowing formula is selected.

$\begin{matrix}{V = \begin{bmatrix}\frac{- 1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\\frac{- 1}{\sqrt{2}} & \frac{- 1}{\sqrt{2}}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 124} \right\rbrack\end{matrix}$

Here, the following formula is satisfied.

$\begin{matrix}{H_{o} = \begin{bmatrix}1 & {- j} \\{- j} & 1\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 125} \right\rbrack\end{matrix}$

Accordingly, the following formula is satisfied.

$\begin{matrix}{U^{H} = {{\frac{V^{H}}{\sqrt{N}} \cdot T^{H} \cdot H_{o}^{H} \cdot W^{H}} = {\begin{bmatrix}\frac{- 1}{2} & \frac{- 1}{2} \\\frac{1}{2} & \frac{- 1}{2}\end{bmatrix} \cdot {\quad{{\begin{bmatrix}1 & 0 \\0 & ^{- {j\Phi}_{1}}\end{bmatrix} \cdot \begin{bmatrix}1 & j \\j & 1\end{bmatrix} \cdot \begin{bmatrix}1 & 0 \\0 & ^{- {j\varphi}_{1}}\end{bmatrix}} = {\quad\begin{bmatrix}\frac{{- 1} - {j}^{- {j\Phi}_{1}}}{2} & \frac{{- {j}^{- {j\varphi}_{1}}} - {j}^{- {j{({\Phi_{1} + \varphi_{1}})}}}}{2} \\\frac{1 - {j}^{- {j\Phi}_{1}}}{2} & \frac{{j}^{- {j\varphi}_{1}} - {j}^{- {j{({\Phi_{1} + \varphi_{1}})}}}}{2}\end{bmatrix}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 126} \right\rbrack\end{matrix}$

In the following, the orthogonal relationship used in [Numeral 114] willbe described.

Here, a product of arbitrary m-row vectors and arbitrary n-columnvectors in the following formula is calculated.

$\begin{matrix}{{H_{o}^{H} \cdot H_{o}} = {\begin{bmatrix}1 & ^{j\frac{\pi}{N}} & \cdots & ^{j\frac{{({N - 1})}^{2}\pi}{N}} \\^{j\frac{\pi}{N}} & 1 & \ddots & ^{j\frac{{({N - 2})}^{2}\pi}{N}} \\\vdots & \ddots & \ddots & \vdots \\^{j\frac{{({N - 1})}^{2}\pi}{N}} & ^{j\frac{{({N - 2})}^{2}\pi}{N}} & \cdots & 1\end{bmatrix} \cdot {\quad\begin{bmatrix}1 & ^{{- j}\frac{\pi}{N}} & \cdots & ^{{- j}\frac{{({N - 1})}^{2}\pi}{N}} \\^{{- j}\frac{\pi}{N}} & 1 & \ddots & ^{{- j}\frac{{({N - 2})}^{2}\pi}{N}} \\\vdots & \ddots & \ddots & \vdots \\^{{- j}\frac{{({N - 1})}^{2}\pi}{N}} & ^{{- j}\frac{{({N - 2})}^{2}\pi}{N}} & \cdots & 1\end{bmatrix}}}} & \left\lbrack {{Numeral}\mspace{14mu} 127} \right\rbrack\end{matrix}$

1) When m<n, the following formula is satisfied.

$\begin{matrix}{{{\sum\limits_{k = 1}^{m}\; {^{j\frac{{({m - k})}^{2}\pi}{N}} \cdot ^{{- j}\frac{{({n - k})}^{2}\pi}{N}}}} + {\sum\limits_{k = {m + 1}}^{n}\; {^{j\frac{{({k - m})}^{2}\pi}{N}} \cdot ^{{- j}\frac{{({n - k})}^{2}\pi}{N}}}} + {\sum\limits_{k = {n + 1}}^{N}\; {^{j\frac{{({k - m})}^{2}\pi}{N}} \cdot ^{{- j}\frac{{({k - n})}^{2}\pi}{N}}}}} = {{\sum\limits_{k = 1}^{N}\; {^{j\frac{{({m - k})}^{2}\pi}{N}} \cdot ^{{- j}\frac{{({n - k})}^{2}\pi}{N}}}} = {{\sum\limits_{k = 1}^{N}^{j\frac{{({m^{2} - n^{2} - {2{k{({m - n})}}}})}\pi}{N}}} = {^{j\frac{{({m^{2} - n^{2}})}\pi}{N}} \cdot {\sum\limits_{k = 1}^{N}^{{- j}\frac{2{k{({m - n})}}\pi}{N}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 128} \right\rbrack\end{matrix}$

Here, it is assumed that the following formula is satisfied.

$\begin{matrix}{S = {{\sum\limits_{k = 1}^{N}\; ^{{- j}\frac{2{k{({m - n})}}\pi}{N}}} = {\sum\limits_{k = 1}^{N}\left( ^{{- j}\frac{2{({m - n})}\pi}{N}} \right)^{k}}}} & \left\lbrack {{Numeral}\mspace{14mu} 129} \right\rbrack\end{matrix}$

In this case, the following formula is satisfied.

$\begin{matrix}{{\left( {1 - ^{{- j}\frac{2{({m - n})}\pi}{N}}} \right) \cdot S} = {{^{{- j}\frac{2{({m - n})}\pi}{N}} - \left( ^{{{- j}\frac{2{({m - n})}\pi}{N}}\;} \right)^{N + 1}} = {{^{{- j}\frac{2{({m - n})}\pi}{N}} \cdot \left\{ {1 - \left( ^{{- j}\frac{2{({m - n})}\pi}{N}} \right)^{N}} \right\}} = {{0\mspace{79mu}\therefore S} = 0}}}} & \left\lbrack {{Numeral}\mspace{14mu} 130} \right\rbrack\end{matrix}$

Thus, the orthogonal relationship is established.

2) When m>n, the following formula is satisfied.

$\begin{matrix}{{{\sum\limits_{k = 1}^{n}{^{j\frac{{({m - k})}^{2}\pi}{N}} \cdot ^{{- j}\frac{{({n - k})}^{2}}{N}}}} + {\sum\limits_{k = {n + 1}}^{m}{^{j\frac{{({m - k})}^{2}\pi}{N}} \cdot ^{{- j}\frac{{({k - n})}^{2}\pi}{N}}}} + {\sum\limits_{k = {m + 1}}^{N}{^{j\frac{{({k - m})}^{2}\pi}{N}} \cdot ^{{- j}\frac{{({k - n})}^{2}\pi}{N}}}}} = {{\sum\limits_{k = 1}^{N}{^{j\frac{{({m - k})}^{2}\pi}{N}} \cdot ^{{- j}\frac{{({n - k})}^{2}\pi}{N}}}} = {{\sum\limits_{k = 1}^{N}^{j\frac{{({m^{2} - n^{2} - {2{k{({m - n})}}}})}\pi}{N}}} = {^{j\frac{{({m^{2} - n^{2}})}\pi}{N}} \cdot {\sum\limits_{k = 1}^{N}^{{- j}\frac{2{k{({m - n})}}\pi}{N}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 131} \right\rbrack\end{matrix}$

Similarly, the following formula is satisfied.

$\begin{matrix}{S = {{\sum\limits_{k = 1}^{N}^{{- j}\frac{2{k{({m - n})}}\pi}{N}}} = {{\sum\limits_{k = 1}^{N}\left( ^{{- j}\frac{2{({m - n})}\pi}{N}} \right)^{k}} = 0}}} & \left\lbrack {{Numeral}\mspace{14mu} 132} \right\rbrack\end{matrix}$

Thus, the orthogonal relationship is established.

From the above, the following formula is obtained.

                                    [Numeral  133]${H_{0}^{H} \cdot H_{0}} = {\begin{bmatrix}1 & ^{j\frac{\pi}{N}} & \ldots & ^{j\frac{{({N - 1})}^{2}\pi}{N}} \\^{j\frac{\pi}{N}} & 1 & \ddots & ^{j\frac{{({N - 2})}^{2}\pi}{N}} \\\vdots & \ddots & \ddots & \vdots \\^{j\frac{{({N - 1})}^{2}\pi}{N}} & ^{j\frac{{({N - 2})}^{2}\pi}{N}} & \ldots & 1\end{bmatrix} \cdot {\quad{\begin{bmatrix}1 & ^{{- j}\frac{\pi}{N}} & \ldots & ^{{- j}\frac{{({N - 1})}^{2}\pi}{N}} \\^{{- j}\frac{\pi}{N}} & 1 & \ddots & ^{{- j}\frac{{({N - 2})}^{2}\pi}{N}} \\\vdots & \ddots & \ddots & \vdots \\^{{- j}\frac{{({N - 1})}^{2}\pi}{N}} & ^{{- j}\frac{{({N - 2})}^{2}\pi}{N}} & \ldots & 1\end{bmatrix} = {N \cdot I}}}}$

The configuration using a plurality of antennas, in which a displacementin the highly sensitive antenna direction occurs and phase noise causeddue to absence of synchronization between carriers in the configurationwhere the local oscillators are provided for respective antennas arecompensated only by the reception side unitary matrix U, andcommunication capacity becomes a multiple of the number of antennas hasbeen described.

In the following, characteristics in a condition where an ideal antennainterval is not set, i.e., where the virtual orthogonal channels havedifferent widths will be described. The fifth example is used as anexample.

[Analysis of Characteristics in SVD Method Based on Line-of-Sight FixedChannels and in Fifth Configuration Example]

(Case where Virtual Orthogonal Channels have Different Widths, whereMatrix Calculation is Performed Only on Reception Side, and where LocalOscillators are Provided Independently for Respective Antennas Both onTransmission and Reception Sides)

Characteristics analysis is performed for the proposed method (fifthexample) in which antenna interval is set based on antenna positionsdifferent from optimum antenna positions for flexibility, whilecomparing to the SVD method.

First, referring to the fifth example, assuming that reception signalvector is r, a signal vector after the matrix calculation on thereception side is represented by the following formula.

U ⁻¹ ·r=U ⁻¹·(H·S+n)=U ⁻¹·(U·Λ ^(1/2) ·S+n)=Λ^(1/2) ·S+U ⁻¹·n∵V=I  [Numeral 134]

where S denotes a transmission signal vector, and n denotes a noisevector.

Further, from the fifth example, the following formula is satisfied.

$\begin{matrix}{U^{- 1} = \begin{bmatrix}{{- j}\; ^{j\; \alpha \frac{\cos {({\alpha/2})}}{\sin \; \alpha}}} & {j\; ^{{- j}\; \varphi \frac{\cos {({\alpha/2})}}{\sin \; \alpha}}} \\{j\; ^{{- j}\; \Phi \frac{\sin {({\alpha/2})}}{\sin \; \alpha}}} & {{- j}\; ^{- {j{({\Phi + \varphi})}}}^{j\; \alpha \frac{\sin {({\alpha/2})}}{\sin \; \alpha}}}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 135} \right\rbrack\end{matrix}$

Accordingly, the transmission signal vector S and noise vector n are setas the following formula.

$\begin{matrix}{{S = \begin{bmatrix}s_{1} \\s_{2}\end{bmatrix}},\mspace{14mu} {n = \begin{bmatrix}n_{1} \\n_{2}\end{bmatrix}}} & \left\lbrack {{Numeral}\mspace{14mu} 136} \right\rbrack\end{matrix}$

Further, normalization is applied to obtain the following formula forcomparison using relative values.

E[|s ₁|² ]=E[|s ₂|²]=1, E[|n ₁|² ]=E[|n ₂|²]=1  [Numeral 137]

Thus, the SNR₁ of λ₁ channel is represented by the following formula.

                                [Numeral  138] $\begin{matrix}{{SNR}_{1} = \frac{{{\lambda_{1} \cdot s_{1}}}^{2}}{E\left\lbrack {{{{- j}\; ^{j\; \alpha}{\frac{\cos \left( {\alpha/2} \right)}{\sin \; \alpha} \cdot n_{1}}} + {j\; ^{{- j}\; \varphi}{\frac{\cos \left( {\alpha/2} \right)}{\sin \; \alpha} \cdot n_{2}}}}}^{2} \right\rbrack}} \\{= {\frac{2 + {2\; \cos \; \alpha}}{\left( {2 \cdot \frac{\cos \left( {\alpha/2} \right)}{\sin \; \alpha}} \right)^{2}} = \frac{4 \cdot {\cos^{2}\left( {\alpha/2} \right)}}{4 \cdot \frac{\cos^{2}\left( {\alpha/2} \right)}{\sin^{2}\alpha}}}} \\{= {\sin^{2}\alpha}}\end{matrix}$

Similarly, the SNR₂ of λ₂ channel is represented by the followingformula.

                                [Numeral  139] $\begin{matrix}{{SNR}_{2} = \frac{{{\lambda_{2} \cdot s_{2}}}^{2}}{E\left\lbrack {{{j\; ^{{- j}\; \Phi}{\frac{\sin \left( {\alpha/2} \right)}{\sin \; \alpha} \cdot n_{1}}} - {j\; ^{- {j{({\Phi + \varphi})}}}^{j\; \alpha}{\frac{\sin \left( {\alpha/2} \right)}{\sin \; \alpha} \cdot n_{2}}}}}^{2} \right\rbrack}} \\{= {\frac{2 - {2\; \cos \; \alpha}}{\left( {2 \cdot \frac{\sin \left( {\alpha/2} \right)}{\sin \; \alpha}} \right)^{2}} = \frac{4 \cdot {\sin^{2}\left( {\alpha/2} \right)}}{4 \cdot \frac{\sin^{2}\left( {\alpha/2} \right)}{\sin^{2}\alpha}}}} \\{= {\sin^{2}\alpha}}\end{matrix}$

Thus, although the orthogonal channels have different widths, both theSNR₁ and SNR₂ become sin² α.

(SVD Method)

For comparison to the fifth example, characteristics analysis of the SVDmethod is performed.

First, from the configuration diagram of FIG. 1, a reception signalvector after unitary matrix calculation according to the SVD method isrepresented by the following formula.

U ^(H) ·r=U ^(H)·(H·V·S+n)=U ^(H)·(U·Λ ^(1/2) ·V ^(H) ·S+n)=Λ^(1/2) ·S+U^(H) ·n  [Numeral 140]

Accordingly, from U^(H) of [Numeral 43], SNR₁ of the λ₁ channel afternormalization is represented by the following formula.

$\begin{matrix}{{SNR}_{1} = {\frac{{{\lambda_{1} \cdot s_{1}}}^{2}}{E\left\lbrack {{{\frac{- ^{j\; {\alpha/2}}}{\sqrt{2}} \cdot n_{1}} + {\frac{- ^{j\; {\alpha/2}}}{\sqrt{2}} \cdot n_{2}}}}^{2} \right\rbrack} = {\frac{2 + {2\; \cos \; \alpha}}{\left( {2 \cdot \frac{1}{\sqrt{2}}} \right)^{2}} = {1 + {\cos \; \alpha}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 141} \right\rbrack\end{matrix}$

Similarly, SNR₂ of λ₂ channel is represented by the following formula.

$\begin{matrix}{{SNR}_{2} = {\frac{{{\lambda_{2} \cdot s_{2}}}^{2}}{E\left\lbrack {{{\frac{{- j}\; ^{j\; {\alpha/2}}}{\sqrt{2}} \cdot n_{1}} + {\frac{j\; ^{j\; {\alpha/2}}}{\sqrt{2}} \cdot n_{2}}}}^{2} \right\rbrack} = {\frac{2 - {2\; \cos \; \alpha}}{\left( {2 \cdot \frac{1}{\sqrt{2}}} \right)^{2}} = {1 - {\cos \; \alpha}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 142} \right\rbrack\end{matrix}$

Thus, the widths of the orthogonal channels are proportional to λ₁=2+2cos α and λ₂=2−2 cos α and, accordingly, the SNR₁ and SNR₂ become 1+1cos α and 1−1 cos α, respectively.

(Comparison Between SNRs of Orthogonal Channels Based on RespectiveMethods in Terms of Antenna Interval)

When the characteristics analysis results of the proposed method (fifthexample) and SVD method are compared with each other in terms of antennaintervals d_(T) and d_(R), a graph of FIG. 9 is obtained. The proposedmethod exhibits the same SNR value between the orthogonal channels λ₁and λ₂ and thus it can be understood that a variation with respect tothe antenna interval is small.

For achievement of a practical and flexible configuration, the analysishas been made with the assumption that matrix calculation processing isperformed only on the reception side so as to eliminate the need to usethe feedback information to be sent to the transmission side in aconfiguration different from one in which there exists an inter-antennaposition at which an eigenvalue is a multiplicity condition to generateda singular point.

Signal power after the matrix calculation on the reception side isproportional to eigenvalue both in the proposed method and SVD method.In the case of the SVD method, the matrix calculation on the receptionside is based on the unitary matrix, so that noise power does not changebut keeps a constant value even if the eigenvalue changes. Therefore,the SNRs of the respective paths in the SNR method become differentvalues which are proportional to the eigenvalue and change in accordancewith the antenna interval.

On the other hand, in the proposed method, the matrix calculation on thereception side is not based on the unitary matrix, so that noise powerchanges in accordance with eigenvalue. Thus, an analysis result of FIG.9 reveals that although signal power exhibits high power and low powerin proportion to the eigenvalue, the SNRs of the respective paths alwaysexhibit the same value and change in accordance with the antennainterval in the same proportion.

Thus, in the proposed method, the SNR with respect to the virtualorthogonal channel does not change even when the antennal intervalchanges and, if a change occurs, the change amount is small, so that itcan be said that the proposed method is more practical and easier to usethan the SVD method.

The content of theoretical analysis with the assumption that the localoscillators are provided independently for respective antennas can betraced to the same modeling also with respect to the movement in thehighly sensitive antenna direction, thus fully covering influence by asubtle change of weather condition such as wind.

Next, arrangement considering actual installation locations will bedescribed. It is likely to be difficult to ensure antenna installationlocation nearer to the user side. On the other hand, it is more likelyto be easier to ensure antenna installation locations on the backbonenetwork side opposed to the user side. In the following, a configurationshown in FIG. 10 in which antenna intervals differ from each otherbetween the transmission and reception side will be described.

FIG. 11, which is obtained by modeling the lower half of the verticallysymmetric channel configuration of FIG. 10 is used to perform analysisas follows.

The distance decay and common phase shift based on atransmitter-receiver distance

R are determined by relative phase shift and therefore can be ignored.In the following, R is set as a reference. Then, the channel differenceof a diagonal channel of angle Δθ₁ with respect to R is represented bythe following formula.

$\begin{matrix}{{{R \cdot \left( {1 - {\cos \left( {\Delta \; \theta_{1}} \right)}} \right)} \approx {R \cdot \left( \frac{\left( {\Delta \; \theta_{1}} \right)^{2}}{2} \right)}} = {{R \cdot \left( {\frac{1}{2}\left( \frac{d_{T} - d_{R}}{2\; R} \right)^{2}} \right)} = {{\frac{\left( {d_{T} - d_{R}} \right)^{2}}{8\; R}\because\frac{\frac{d_{T}}{2} - \frac{d_{R}}{2}}{R}} = {\frac{d_{T} - d_{R}}{2\; R} = {{\tan \left( {\Delta \; \theta_{1}} \right)} \approx \left( {\Delta \; \theta_{1}} \right)}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 143} \right\rbrack\end{matrix}$

Similarly, the channel difference of a diagonal channel of angle Δθ₂with respect to R is represented by the following formula.

$\begin{matrix}{{{R \cdot \left( {1 - {\cos \left( {\Delta \; \theta_{1}} \right)}} \right)} \approx {R \cdot \left( \frac{\left( {\Delta \; \theta_{2}} \right)^{2}}{2} \right)}} = {{R \cdot \left( {\frac{1}{2}\left( \frac{d_{T} - d_{R}}{2\; R} \right)^{2}} \right)} = {{\frac{\left( {d_{T} - d_{R}} \right)^{2}}{8\; R}\because\frac{\frac{d_{T}}{2} - \frac{d_{R}}{2}}{R}} = {\frac{d_{T} - d_{R}}{2\; R} = {{\tan \left( {\Delta \; \theta_{2}} \right)} \approx \left( {\Delta \; \theta_{2}} \right)}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 144} \right\rbrack\end{matrix}$

The phase rotation a resulting from the channel difference between twowaves at the reception points is represented by the following formula.

$\begin{matrix}{\alpha = {{2\; {{\pi\left( \frac{\left( {d_{T} + d_{R}} \right)^{2} - \left( {d_{T} - d_{R}} \right)^{2}}{{8R}\;} \right)}/\gamma}} = {{\frac{\pi}{\gamma} \cdot \frac{4 \cdot d_{T} \cdot d_{R}}{4 \cdot R}} = {\frac{\pi}{\gamma} \cdot \frac{d_{T} \cdot d_{R}}{R}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 145} \right\rbrack\end{matrix}$

Incidentally, assuming that RF frequency=30 GHz, R=2000 m, d_(T)=5 m,and d_(R)=2 m, the following formula is satisfied.

$\begin{matrix}{\alpha = {{\frac{\pi}{\gamma} \cdot \frac{d_{T} \cdot d_{R}}{R}} = {{\frac{\pi}{\left( {3 \cdot 10^{8}} \right)/\left( {30 \cdot 10^{9}} \right)} \cdot \frac{5 \times 2}{2000}} = \frac{\pi}{2}}}} & \left\lbrack {{Numeral}\mspace{14mu} 146} \right\rbrack\end{matrix}$

With phase shift Φ caused due to a positional variation of an antennafor transmitting a signal s₂ taken into consideration, the channelmatrix H normalized by the diagonal channel of angle Δθ₁ is representedby the following formula.

$\begin{matrix}{H = \begin{bmatrix}1 & {^{{- j}\; \alpha} \cdot ^{j\; \Phi}} \\^{{- j}\; \alpha} & {1 \cdot ^{j\; \Phi}}\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 147} \right\rbrack\end{matrix}$

Thus, the same condition as results that have so far been obtained isexhibited.

Further, from the following [Numeral 148], [Numeral 149] is obtained.

$\begin{matrix}\begin{matrix}{\Omega = {{H^{H} \cdot H} = {{\begin{bmatrix}1 & ^{j\; \alpha} \\{^{j\alpha} \cdot ^{- {j\Phi}}} & ^{- {j\Phi}}\end{bmatrix} \cdot \begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\Phi}} \\^{- {j\alpha}} & ^{j\Phi}\end{bmatrix}} =}}} \\{\begin{bmatrix}2 & {^{j\Phi}\left( {^{j\alpha} + ^{- {j\alpha}}} \right)} \\{^{- {j\Phi}}\left( {^{j\alpha} + ^{- {j\alpha}}} \right)} & 2\end{bmatrix}} \\{= \begin{bmatrix}2 & {{2 \cdot \cos}\; {\alpha \cdot ^{j\Phi}}} \\{{2 \cdot \cos}\; {\alpha \cdot ^{- {j\Phi}}}} & 2\end{bmatrix}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 148} \right\rbrack \\{{\begin{matrix}{2 - \lambda} & {{2 \cdot \cos}\; {\alpha \cdot ^{j\Phi}}} \\{{2 \cdot \cos}\; {\alpha \cdot ^{- {j\Phi}}}} & {2 - \lambda}\end{matrix}} = {{\lambda^{2} + 4 - {4\; \lambda} - {4\; \cos^{2}\alpha}} = {{\lambda^{2} - {4\; \lambda} - {4\; \sin^{2}\alpha}} = {{0\therefore\lambda} = {{2 \pm \sqrt{4 - {4\; \sin^{2}\alpha}}} = {2 \pm {2\; \cos \; \alpha}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 149} \right\rbrack\end{matrix}$

FIG. 12 is a graph showing this result. When α=(π/λ)·(d_(R)²/R)->α=(π/λ)·(d_(T)·d_(R)/R) is constructed from the above result, thesame result is obtained. Thus, it can be understood that the proposedmethod can be used without modification.

A case where a diamond-shaped misalignment occurs in the antennaarrangement direction between the transmission and reception antennaswill be described.

In FIG. 13, R is set as a reference, as in the above case. Then, channeldifferences of diagonal channels d₁₁, d₁₂, d₂₁, and d₂₂ with respect toR are represented as follows.

In the case of d₁₁;

$\begin{matrix}{{{R \cdot \left( {1 - {\cos \left( {\Delta \; \theta_{11}} \right)}} \right)} \approx {R \cdot \left( \frac{\left( {\Delta \; \theta_{11}} \right)^{2}}{2} \right)}} = {{R \cdot \left( {\frac{1}{2}\left( \frac{_{0}}{R} \right)^{2}} \right)} = {{\frac{_{0}^{2}}{2\; R}\because\frac{_{0}}{R}} = {{\tan \left( {\Delta \; \theta_{11}} \right)} \approx \left( {\Delta \; \theta_{11}} \right)}}}} & \left\lbrack {{Numeral}\mspace{14mu} 150} \right\rbrack\end{matrix}$

In the case of d₁₂;

$\begin{matrix}{{{R \cdot \left( {1 - {\cos \left( {\Delta \; \theta_{12}} \right)}} \right)} \approx {R \cdot \left( \frac{\left( {\Delta \; \theta_{12}} \right)^{2}}{2} \right)}} = {{R \cdot \left( {\frac{1}{2}\left( \frac{{+ _{0}}}{R} \right)^{2}} \right)} = {\frac{\left( {{+ _{0}}} \right)^{2}}{2\; R} = {{\frac{{^{2}{+ {_{0}^{2}{+ 2}}}}\; {_{0}}}{2\; R}\because\frac{{+ _{0}}}{R}} = {{\tan \left( {\Delta \; \theta_{12}} \right)} \approx \left( {\Delta \; \theta_{12}} \right)}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 151} \right\rbrack\end{matrix}$

In the case of d₂₁;

$\begin{matrix}{{{R \cdot \left( {1 - {\cos \left( {\Delta \; \theta_{21}} \right)}} \right)} \approx {R \cdot \left( \frac{\left( {\Delta \; \theta_{21}} \right)^{2}}{2} \right)}} = {{R \cdot \left( {\frac{1}{2}\left( \frac{{- _{0}}}{R} \right)^{2}} \right)} = {\frac{\left( {{- _{0}}} \right)^{2}}{2\; R} = {{\frac{{^{2}{+ {_{0}^{2}{- 2}}}}{_{0}}}{2\; R}\because\frac{{- _{0}}}{R}} = {{\tan \left( {\Delta \; \theta_{21}} \right)} \approx \left( {\Delta \; \theta_{21}} \right)}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 152} \right\rbrack\end{matrix}$

In the case of d₂₂;

$\begin{matrix}{{{R \cdot \left( {1 - {\cos \left( {\Delta \; \theta_{22}} \right)}} \right)} \approx {R \cdot \left( \frac{\left( {\Delta \; \theta_{22}} \right)^{2}}{2} \right)}} = {{R \cdot \left( {\frac{1}{2}\left( \frac{_{0}}{R} \right)^{2}} \right)} = {{\frac{_{0}^{2}}{2\; R}\because\frac{_{0}}{R}} = {{\tan \left( {\Delta \; \theta_{22}} \right)} \approx \left( {\Delta \; \theta_{22}} \right)}}}} & \left\lbrack {{Numeral}\mspace{14mu} 153} \right\rbrack\end{matrix}$

Assuming that that the phase rotation resulting from the channeldifference is represented by α=2π(d²/2R)/γ=(π/γ)·(d²/R),ζ=2π(2·d·d₀/2R)/γ=(π/γ)·(2·d·d₀/R), the channel matrix H normalized bythe channel d₁₁ is represented by the following formula.

$\begin{matrix}{H = \begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\; \xi}} \\{^{- {j\alpha}} \cdot ^{- {j\xi}}} & 1\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 154} \right\rbrack\end{matrix}$

Accordingly, the following formula is obtained.

$\begin{matrix}\begin{matrix}{\Omega = {{H^{H} \cdot H} = {\begin{bmatrix}1 & {^{j\; \alpha} \cdot ^{j\xi}} \\{^{j\alpha} \cdot ^{- {j\xi}}} & 1\end{bmatrix} \cdot}}} \\{{\begin{bmatrix}1 & {^{- {j\alpha}} \cdot ^{j\xi}} \\{^{- {j\alpha}} \cdot ^{- {j\xi}}} & 1\end{bmatrix} =}} \\{\begin{bmatrix}2 & {^{j\xi}\left( {^{j\alpha} + ^{- {j\alpha}}} \right)} \\{^{- {j\xi}}\left( {^{j\alpha} + ^{- {j\alpha}}} \right)} & 2\end{bmatrix}} \\{= \begin{bmatrix}2 & {{2 \cdot \cos}\; {\alpha \cdot ^{j\xi}}} \\{{2 \cdot \cos}\; {\alpha \cdot ^{- {j\xi}}}} & 2\end{bmatrix}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 155} \right\rbrack\end{matrix}$

From the above, the following formula is obtained.

$\begin{matrix}{{\begin{matrix}{2 - \gamma} & {{2 \cdot \cos}\; {\alpha \cdot ^{j\xi}}} \\{{2 \cdot \cos}\; {\alpha \cdot ^{- {j\xi}}}} & {2 - \gamma}\end{matrix}} = {{\gamma^{2} + 4 - {4\; \gamma} - {4\; \cos^{2}\alpha}} = {{\gamma^{2} - {4\; \gamma} - {4\; \sin^{2}\alpha}} = {{0\therefore\gamma} = {{2 \pm \sqrt{4 - {4\; \sin^{2}\alpha}}} = {2 \pm {2\; \cos \; \alpha}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 156} \right\rbrack\end{matrix}$

Thus, it can be understood that even if a diamond-shaped misalignmentoccurs, there is no influence on the eigenvalues corresponding to thewidths of the respective paths.

(Singular Value Decomposition H=U·Λ^(1/2)·V^(H))

The singular value decomposition of the channel matrix H is representedby the following formula.

$\begin{matrix}\begin{matrix}{H = {{U \cdot \Lambda^{1\text{/}2} \cdot V^{H}} = {\begin{bmatrix}\frac{- ^{{- j}\; \frac{\alpha}{2}}}{\sqrt{2}} & \frac{j \cdot ^{{- j}\; \frac{\alpha}{2}}}{\sqrt{2}} \\\frac{\begin{matrix}{{- ^{{- j}\; \frac{\alpha}{2}}} \cdot} \\^{- {j\xi}}\end{matrix}}{\sqrt{2}} & \frac{\begin{matrix}{{- j} \cdot ^{{- j}\; \frac{\alpha}{2}} \cdot} \\^{{- j}\; \xi}\end{matrix}}{\sqrt{2}}\end{bmatrix} \cdot}}} \\{{\begin{bmatrix}\left( {^{j\; \frac{\alpha}{2}} + ^{{- j}\; \frac{\alpha}{2}}} \right) & 0 \\0 & {- {j\left( {^{j\; \frac{\alpha}{2}} - ^{{- j}\; \frac{\alpha}{2}}} \right)}}\end{bmatrix} \cdot}} \\{\begin{bmatrix}\frac{- 1}{\sqrt{2}} & \frac{- ^{j\xi}}{\sqrt{2}} \\\frac{1}{\sqrt{2}} & \frac{- ^{j\xi}}{\sqrt{2}}\end{bmatrix}} \\{= {\begin{bmatrix}\frac{- \left( {1 + ^{- {j\alpha}}} \right)}{\sqrt{2}} & \frac{\left( {1 - ^{- {j\alpha}}} \right)}{\sqrt{2}} \\\frac{\begin{matrix}{{- \left( {1 + ^{- {j\alpha}}} \right)} \cdot} \\^{- {j\xi}}\end{matrix}}{\sqrt{2}} & \frac{\begin{matrix}{{- \left( {1 - ^{- {j\alpha}}} \right)} \cdot} \\^{- {j\xi}}\end{matrix}}{\sqrt{2}}\end{bmatrix} \cdot}} \\{{\begin{bmatrix}\frac{- 1}{\sqrt{2}} & \frac{- ^{j\xi}}{\sqrt{2}} \\\frac{1}{\sqrt{2}} & \frac{- ^{j\xi}}{\sqrt{2}}\end{bmatrix} = \begin{bmatrix}1 & \begin{matrix}{^{- {j\alpha}} \cdot} \\^{j\xi}\end{matrix} \\\begin{matrix}{^{- {j\alpha}} \cdot} \\^{- {j\xi}}\end{matrix} & 1\end{bmatrix}}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 157} \right\rbrack\end{matrix}$

Further, the U and V are represented by the following formulas.

$\begin{matrix}{{U^{H} \cdot U} = {\begin{bmatrix}\frac{- ^{j\frac{\alpha}{2}}}{\sqrt{2}} & \frac{{- ^{j\frac{\alpha}{2}}} \cdot ^{j\xi}}{\sqrt{2}} \\\frac{{- j} \cdot ^{j\; \frac{\alpha}{2}}}{\sqrt{2}} & \frac{j \cdot ^{j\; \frac{\alpha}{2}} \cdot ^{j\; \xi}}{\sqrt{2}}\end{bmatrix} \cdot {\quad{\left\lbrack \begin{matrix}\frac{- ^{{- j}\; \frac{\alpha}{2}}}{\sqrt{2}} & \frac{j \cdot ^{{- j}\; \frac{\alpha}{2}}}{\sqrt{2}} \\\frac{{- ^{{- j}\; \frac{\alpha}{2}}} \cdot ^{- {j\xi}}}{\sqrt{2}} & \frac{{- j} \cdot ^{{- j}\; \frac{\alpha}{2}} \cdot ^{- {j\xi}}}{\sqrt{2}}\end{matrix} \right\rbrack  = {{\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}{V \cdot V^{H}}} = {{\begin{bmatrix}\frac{- 1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\\frac{- ^{- {j\xi}}}{\sqrt{2}} & \frac{- ^{- {j\xi}}}{\sqrt{2}}\end{bmatrix} \cdot \begin{bmatrix}\frac{- 1}{\sqrt{2}} & \frac{- ^{j\xi}}{\sqrt{2}} \\\frac{1}{\sqrt{2}} & \frac{- ^{j\xi}}{\sqrt{2}}\end{bmatrix}} = \left\lbrack \begin{matrix}1 & 0 \\0 & 1\end{matrix} \right\rbrack}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 158} \right\rbrack\end{matrix}$

Thus, it can be confirmed that the singular value decomposition of H isachieved by the unitary matrixes of U and V. That is, even if adiamond-shaped misalignment occurs, the eigenvalues corresponding to thewidths of the respective paths before generation of the misalignment canbe kept, and the singular value decomposition of H is achieved by theunitary matrixes of U and V. It goes without saying that the sameconfiguration as above can be obtained even if the phase shift Φ iscaused due to a positional variation of a transmission antenna.

[Case where Matrix Calculation is Performed Only on Reception Side andwhere Antenna Arrangement Between Transmission/Reception Sides is Formedin Diamond Shape]

Next, how the proposed method in which the matrix calculation isperformed only on the reception end operates in the case where such adiamond-shaped misalignment occurs will be described.

A case where a diamond-shaped misalignment occurs in the antennaarrangement direction between transmission and reception antennas in theconfiguration according to the present invention in which the matrixcalculation is performed only on the reception side will be descried.Here, the diamond-shaped channel matrix H obtained in the aboveexamination is used without modification.

From FIG. 14, considering an inter-antenna position where e^(jα)=j issatisfied, singular value diagonal matrix Λ^(1/2) and channel matrix Hare represented by the following formulas.

[Singular Value Diagonal Matrix Λ^(1/2)]

$\begin{matrix}{\Lambda^{1\text{/}2} = {\left\lbrack \begin{matrix}\sqrt{\lambda_{1}} & 0 \\0 & \sqrt{\lambda_{2}}\end{matrix} \right\rbrack = {\left\lbrack \begin{matrix}\sqrt{2 + {2\; \cos \; \alpha}} & 0 \\0 & \sqrt{2 - {2\; \cos \; \alpha}}\end{matrix} \right\rbrack = {\quad\left\lbrack \begin{matrix}\sqrt{2} & 0 \\0 & \sqrt{2}\end{matrix} \right\rbrack}}}} & \left\lbrack {{Numeral}\mspace{14mu} 159} \right\rbrack\end{matrix}$

[Channel Matrix H]

$\begin{matrix}{{{H = {\begin{bmatrix}1 & {{- j} \cdot ^{j\xi}} \\{{- j} \cdot ^{- {j\xi}}} & 1\end{bmatrix} = {{U \cdot \Lambda^{1\text{/}2} \cdot V^{H}} = {{U \cdot \begin{bmatrix}\sqrt{2} & 0 \\0 & \sqrt{2}\end{bmatrix} \cdot \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}\mspace{14mu} {where}}}}}; {\alpha = \frac{\pi}{2}}},{\xi = {{\frac{2{\pi \cdot {{\cdot _{0}}}}}{\gamma \; R}\therefore U} = {\begin{bmatrix}U_{11} & U_{12} \\U_{21} & U_{22}\end{bmatrix} = {\begin{bmatrix}1 & {{- j} \cdot ^{j\xi}} \\{{- j} \cdot ^{- {j\xi}}} & 1\end{bmatrix} \cdot {\quad{{{\left\lbrack \begin{matrix}{1\text{/}\sqrt{2}} & 0 \\0 & {1\text{/}\sqrt{2}}\end{matrix} \right\rbrack  = {{\begin{bmatrix}{1\text{/}\sqrt{2}} & {{{- j} \cdot ^{j\xi}}\text{/}\sqrt{2}} \\{{{- j} \cdot ^{- {j\xi}}}\text{/}\sqrt{2}} & {1\text{/}\sqrt{2}}\end{bmatrix}\therefore U^{H}} = {\begin{bmatrix}{1\text{/}\sqrt{2}} & {{j \cdot ^{j\xi}}\text{/}\sqrt{2}} \\{{j \cdot ^{- {j\xi}}}\text{/}\sqrt{2}} & {1\text{/}\sqrt{2}}\end{bmatrix}\mspace{14mu} {where}}}}; {\alpha = {{\frac{\pi}{\gamma} \cdot \frac{^{2}}{R}} = \frac{\pi}{2}}}},{\xi = \frac{2\; {\pi \cdot {{\cdot _{0}}}}}{\gamma \; R}}}}}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 160} \right\rbrack\end{matrix}$

Here, the following equation is satisfied.

$\begin{matrix}{{U^{H} \cdot U} = {\begin{bmatrix}{1\text{/}\sqrt{2}} & {{j \cdot ^{j\xi}}\text{/}\sqrt{2}} \\{{j \cdot ^{- {j\xi}}}\text{/}\sqrt{2}} & {1\text{/}\sqrt{2}}\end{bmatrix} \cdot {\quad{\left\lbrack \begin{matrix}{1\text{/}\sqrt{2}} & {{{- j} \cdot ^{j\xi}}\text{/}\sqrt{2}} \\{{{- j} \cdot ^{- {j\xi}}}\text{/}\sqrt{2}} & {1\text{/}\sqrt{2}}\end{matrix} \right\rbrack  = \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 161} \right\rbrack\end{matrix}$

Thus, even if a diamond-shaped misalignment occurs, the configuration inwhich the matrix calculation is performed only on the reception side iseffected. Note that even if phase shift Φ or φ is caused by the localoscillators or due to antenna position displacement, the sameconfiguration as above can be obtained.

[Case where Antenna Arrangement Shape Between Transmission/ReceptionSides is Further Generalized]

A case where the antenna arrangement shape between the transmission andreception sides is further generalized will be described. This is anapplication example, including a wireless LAN or the like constructed ina line-of-sight communication system, having high flexibility ofinstallation position.

From FIG. 15, the following formulas are obtained.

$\begin{matrix}{{d_{11} = R}{d_{12} = {\left\{ {\left( {R - {d_{T\;}\; {\cos \left( \theta_{T} \right)}}} \right)^{2} + \left( {d_{T}\mspace{11mu} {\sin \left( \theta_{T} \right)}} \right)^{2}} \right\}^{1\text{/}2} \approx {\left( {R - {d_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}}} \right)\left( {1 + \frac{\left( {_{T}\mspace{11mu} {\sin \left( \theta_{T} \right)}} \right)^{2}}{2\left( {R - {_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}}} \right)^{2}}} \right)} \approx {R - {d_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}} + \frac{\left( {_{T}\mspace{11mu} {\sin \left( \theta_{T} \right)}} \right)^{2}}{2\left( {R - {_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}}} \right)}} \approx {R - {d_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}} + \frac{\left( {_{T}\mspace{11mu} {\sin \left( \theta_{T} \right)}} \right)^{2}}{2\; R}}}}{d_{21} = {\left\{ {\left( {R + {d_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}}} \right)^{2} + \left( {d_{R}\mspace{11mu} {\sin \left( \theta_{R} \right)}} \right)^{2}} \right\}^{1\text{/}2} \approx {\left( {R + {d_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}}} \right)\left( {1 + \frac{\left( {_{R}\mspace{11mu} {\sin \left( \theta_{R} \right)}} \right)^{2}}{2\left( {R + {_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}}} \right)^{2}}} \right)} \approx {R + {d_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}} + \frac{\left( {_{R}\mspace{11mu} {\sin \left( \theta_{R} \right)}} \right)^{2}}{2\left( {R + {_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}}} \right)}} \approx {R + {d_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}} + \frac{\left( {_{R}\mspace{11mu} {\sin \left( \theta_{R} \right)}} \right)^{2}}{2\; R}}}}{d_{22} = \left\{ {{\left( {R - {d_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}} + {d_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}}} \right)^{2} + \left( {{d_{R}\mspace{11mu} {\sin \left( \theta_{R} \right)}} - \left. \quad{d_{T}\mspace{11mu} {\sin \left( \theta_{T} \right)}} \right)^{2}} \right\}^{1\text{/}2}} \approx {\left( {R - {d_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}} + {d_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}}} \right) \left( {1 + \frac{\left( {{_{R}\mspace{11mu} {\sin \left( \theta_{R} \right)}} - {_{T}\mspace{11mu} {\sin \left( \theta_{T} \right)}}} \right)^{2}}{2\left( {R - {_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}} + {_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}}} \right)^{2}}} \right)} \approx {R - {d_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}} + {d_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}} + \frac{\left( {{_{R}\mspace{11mu} {\sin \left( \theta_{R} \right)}} - {_{T}\mspace{11mu} {\sin \left( \theta_{T} \right)}}} \right)^{2}}{2\left( {R - {_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}} + {_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}}} \right)}} \approx {R - {d_{T}\mspace{11mu} {\cos \left( \theta_{T} \right)}} + {d_{R}\mspace{11mu} {\cos \left( \theta_{R} \right)}} + \frac{\left( {{_{R}\mspace{11mu} {\sin \left( \theta_{R} \right)}} - {_{T}\mspace{11mu} {\sin \left( \theta_{T} \right)}}} \right)^{2}}{2\; R}}} \right.}} & \left\lbrack {{Numeral}\mspace{14mu} 162} \right\rbrack\end{matrix}$

Further, from FIG. 15, the channel matrix H focusing only on a phasedifference between reception antennas is represented by the followingformula.

$\begin{matrix}{H = \begin{bmatrix}1 & ^{j - {\frac{2\; \pi}{\gamma}{({d_{12} - d_{11}})}}} \\^{j - {\frac{2\; \pi}{\gamma}{({d_{21} - d_{22}})}}} & 1\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 163} \right\rbrack\end{matrix}$

From the above, the following formula is obtained.

$\begin{matrix}\begin{matrix}{\Omega = {H^{H} \cdot H}} \\{= {\begin{bmatrix}1 & ^{j\frac{2\; \pi}{\gamma}{({d_{21} - d_{22}})}} \\^{j\frac{2\; \pi}{\gamma}{({d_{12} - d_{11}})}} & 1\end{bmatrix} \cdot}} \\{\begin{bmatrix}1 & ^{j - {\frac{2\; \pi}{\gamma}{({d_{12} - d_{11}})}}} \\^{j - {\frac{2\; \pi}{\gamma}{({d_{21} - d_{22}})}}} & 1\end{bmatrix}} \\{= \left. \begin{bmatrix}2 & \begin{matrix}{^{j - {\frac{2\; \pi}{\gamma}{({d_{12} - d_{11}})}}} +} \\^{j\frac{2\; \pi}{\gamma}{({d_{21} - d_{22}})}}\end{matrix} \\\begin{matrix}{^{j\frac{2\; \pi}{\gamma}{({d_{12} - d_{11}})}} +} \\^{j - {\frac{2\; \pi}{\gamma}{({d_{21} - d_{22}})}}}\end{matrix} & 2\end{bmatrix}\Rightarrow\begin{bmatrix}2 & 0 \\0 & 2\end{bmatrix} \right.}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 164} \right\rbrack\end{matrix}$

Thus, in order for the eigenvalue to be a multiplicity condition, it isonly necessary for the first term, i.e., (2π/γ)·(d₁₂−d₁₁) and the secondterm, i.e., −(2π/γ)·(d₂₁−d₂₂) to have inversed phases with each other.That is, since (2π/γ)·(d₁₂−d₁₁)=−(2π/γ)·(d₂₁−d₂₂) mod 20π is satisfied,or a difference between the first and second terms is π, the followingformula is satisfied.

$\begin{matrix}{{{\frac{2\; \pi}{\gamma}\left( {d_{12} - d_{11}} \right)} + {\frac{2\; \pi}{\gamma}\left( {d_{21} - d_{22}} \right)}} = {\pi \mspace{14mu} {mod}\; 2\; \pi}} & \left\lbrack {{Numeral}\mspace{14mu} 165} \right\rbrack\end{matrix}$

From the above, the following formula is obtained.

$\begin{matrix}{{\therefore{\frac{2\; \pi}{\gamma}{{d_{12} - d_{11} + d_{21} - d_{22}}}}} = {{{{{\pi \left( {{2\; n} + 1} \right)}\mspace{14mu} n} \in Z^{+}}\therefore{{d_{12} - d_{11} + d_{21} - d_{22}}}} = {{\frac{\gamma}{2}\left( {{2\; n} + 1} \right)\mspace{14mu} n} \in Z^{+}}}} & \left\lbrack {{Numeral}\mspace{14mu} 166} \right\rbrack\end{matrix}$

When d₁₁ to d₂₂ are assigned to the obtained relationship, the followingformula is satisfied.

$\begin{matrix}{{{d_{12} - d_{11} + d_{21} - d_{22}}} = {{{{{- d_{T}}{\cos \left( \theta_{T} \right)}\frac{\left( {d_{T}{\sin \left( \theta_{T} \right)}} \right)^{2}}{2\; R}} + \frac{\left( {d_{R}{\sin \left( \theta_{R} \right)}} \right)^{2}}{2\; R} + {d_{T}{\cos \left( \theta_{T} \right)}} - \frac{\left( {d_{R}{\sin \left( \theta_{R} \right)}} \right)^{2} - \left( {d_{T}{\sin \left( \theta_{T} \right)}} \right)^{2}}{2\; R}}} = {{{\frac{\left( {d_{T}{\sin \left( \theta_{T} \right)}} \right)^{2}}{2\; R} + \frac{\left( {d_{R}{\sin \left( \theta_{R} \right)}} \right)^{2}}{2\; R} + \frac{\left( {d_{R}{\sin \left( \theta_{R} \right)}} \right)^{2} - \left( {d_{T}{\sin \left( \theta_{T} \right)}} \right)^{2}}{2\; R}}} = {{\frac{{{- 2} \cdot d_{T} \cdot d_{R}}{{\sin \left( \theta_{T} \right)} \cdot {\sin \left( \theta_{R} \right)}}}{2\; R}} = \frac{{d_{T} \cdot d_{R}}{{\sin \left( \theta_{T} \right)} \cdot {\sin \left( \theta_{R} \right)}}}{R}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 167} \right\rbrack\end{matrix}$

Accordingly, the following formula is obtained.

$\begin{matrix}{\frac{d_{T} \cdot d_{R} \cdot {\sin \left( \theta_{T} \right)} \cdot {\sin \left( \theta_{R} \right)}}{R} = {{\frac{\gamma}{2}\left( {{2\; n} + 1} \right)\mspace{14mu} n} \in Z^{+}}} & \left\{ {{Numeral}\mspace{14mu} 168} \right\}\end{matrix}$

Thus, as a condition that the eigenvalue becomes a multiplicitycondition, the following formula is obtained.

$\begin{matrix}{{\therefore{d_{T} \cdot d_{R}}} = {{{\frac{R}{{\sin \left( \theta_{T} \right)} \cdot {\sin \left( \theta_{R} \right)}} \cdot \gamma \cdot \left( {n + \frac{1}{2}} \right)}\mspace{14mu} n} \in Z^{+}}} & \left\lbrack {{Numeral}\mspace{14mu} 169} \right\rbrack\end{matrix}$

Various antenna configuration can be possible with the paths having thesame width as long as the above condition is satisfied. It should benoted that definitions of the R used here and abovementioned R areslightly different from each other.

In the above description, the pilot signals are used as a detectionmeans for detecting a positional variation in the antennas or channelscaused by external factors or a phase variation caused due to use of thelocal oscillators provided independently for respective antennas.However, the above variations can be detected by a configuration notusing the pilot signals. For example, a method that uses data forconveying information may be employed. Further, although not shown, amethod that estimates a phase variation using a determination resultafter equalization or method that estimates a phase variation byre-encoding a signal after error correction may be employed. In thefollowing, the method that detects the above variations without use ofthe pilot signals will be described taking a case where two antennas areused as an example.

Here, description is made using the channel matrix described above, i e,channel matrix represented by the following formula.

$\begin{matrix}{H = \begin{bmatrix}1 & {{- j} \cdot ^{j\; \Phi}} \\{{- j} \cdot ^{j\; \varphi}} & {1 \cdot ^{j{({\Phi + \varphi})}}}\end{bmatrix}} & \left\{ {{Numeral}\mspace{14mu} 170} \right\}\end{matrix}$

It is assumed that transmission and reception signal vectors arerepresented by the following formulas.

$\begin{matrix}{{S = \begin{bmatrix}s_{1} \\s_{2}\end{bmatrix}},{Y = \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}}} & \left\lbrack {{Numeral}\mspace{14mu} 171} \right\rbrack\end{matrix}$

In this case, the following formula is obtained.

$\begin{matrix}{Y = {\begin{bmatrix}y_{1} \\y_{2}\end{bmatrix} = {{H \cdot S} = {\begin{bmatrix}1 & {{–j} \cdot ^{j\; \Phi}} \\{{–j} \cdot ^{j\; \varphi}} & {1 \cdot ^{j{({\Phi + \varphi})}}}\end{bmatrix} \cdot \begin{bmatrix}s_{1} \\s_{2}\end{bmatrix}}}}} & \left\lbrack {{Numeral}\mspace{14mu} 172} \right\rbrack\end{matrix}$

Assuming that s₁ and s₂ in the above formula have been obtained properlyfrom a determination result after equalization or signal reproductionafter error correction, [Numeral 174] is obtained from the relationshiprepresented by [Numeral 173].

$\begin{matrix}{y_{1} = {s_{1} - {j \cdot ^{j\; \Phi} \cdot s_{2}}}} & \left\lbrack {{Numeral}\mspace{14mu} 173} \right\rbrack \\{^{j\; \Phi} = \frac{s_{1} - y_{1}}{j \cdot s_{2}}} & \left\lbrack {{Numeral}\mspace{14mu} 174} \right\rbrack\end{matrix}$

Thus, Φ can be detected.

Then, the detected Φ is used. Before that, from the relationshiprepresented by [Numeral 172], the following formula is satisfied.

y ₂ =−j·e ^(jφ) ·s ₁ +e ^(j(Φ+φ)) ·s ₂  [Numeral 175]

Accordingly, the following formula is obtained.

$\begin{matrix}{^{j\; \varphi} = \frac{y_{2}}{{^{j\; \Phi} \cdot s_{2}} - {j \cdot s_{1}}}} & \left\lbrack {{Numeral}\mspace{14mu} 176} \right\rbrack\end{matrix}$

Thus, φ can be detected.

As described above, not by using pilot signal, but by using dataconveying information, it is possible to detect a positional variationin the antennas or channels caused by external factors or a phasevariation caused due to use of the local oscillators providedindependently for respective antennas. In the above example, operationafter start-up processing has been described. That is, once the start-upprocessing is completed, data flows constantly, so that the detection ofa phase variation is constantly executed.

[Actual Radio Wave Propagation Model]

The above results have been obtained in the configuration where only thedirect wave is taken into consideration. In the actual radio wavepropagation environment, a reflected wave exists. FIG. 16 is a viewshowing a propagation model used in the fixed point microwavecommunication, called three-ray model. The three-ray model is composedof duct wave, ground reflected wave, and direct wave. Assuming that theduct wave can be ignored depending on the distance between transmissionand reception stations or beam width of antennas to be used, thethree-ray model can be approximated as two-ray model composed of theground reflected wave and direct wave. Thus, the following descriptionwill be made with the actual radio wave propagation model regarded astwo-ray model.

First, as shown in FIG. 17, the ideal operating condition of the MIMO inthe line-of-sight radio wave propagation model where the groundreflected wave exists is defined as follows.

It is assumed that even when the matrix calculation (channel matrixcalculation processing means) for construction of orthogonal channelsperformed for the direct wave is applied to delayed wave, the orthogonalchannels can be formed.

In FIG. 17, black lines represent the direct wave, and brown linesrepresent the delayed wave corresponding to the ground reflected wave.

[Case where MIMO Antennas are Horizontally Arranged]

An example in which the MIMO antennas are horizontally arranged in thetwo-ray model composed of the ground reflected wave and direct wave isshown in FIG. 18.

FIG. 19 shows the arrangement of FIG. 18 as viewed from directly aboveand as viewed edge-on. In FIG. 18, the upper lines represent the directwave, lower lines represent the ground reflected wave, and double linesrepresent a diagonal channel in the MIMO.

It is assumed, in FIGS. 18 and 19, that the MIMO antennas are arrangedso that virtual orthogonal channels can be constructed by the matrixcalculation performed only for the direct wave.

That is, as described above, it is assumed that, with respect to thechannel difference ΔR=d²/(2R) between the direct waves, the phaserotation a resulting from the channel difference has the relationship:α=(π/λ)·(d²/R), and the matrix calculation is processed based on therelationship.

The channel difference between the ground reflected waves is calculatedas follows.

Assuming that the antenna height from the ground is L, the channeldifference ΔR_(r) between the ground reflected waves is represented bythe following formula.

$\begin{matrix}\begin{matrix}{{\Delta \; R_{r}} = {2 \cdot \left( {\sqrt{\left( \frac{R + {\Delta \; R}}{2} \right)^{2} + L^{2}} - \sqrt{\left( \frac{R}{2} \right)^{2} + L^{2}}} \right)}} \\{= {2 \cdot \sqrt{\left( {R^{2}/4} \right) + L^{2}} \cdot \left( {\sqrt{\frac{\begin{matrix}{\left( {R^{2}/4} \right) +} \\{\left( {{R \cdot \Delta}\; {R/2}} \right) +} \\{\left( {\Delta \; {R^{2}/4}} \right) + L^{2}}\end{matrix}}{\left( {R^{2}/4} \right) + L^{2}}} - 1} \right)}} \\{= {2 \cdot \sqrt{\left( {R^{2}/4} \right) + L^{2}} \cdot \left( {\sqrt{1 + \frac{\begin{matrix}{\left( {{R \cdot \Delta}\; {R/2}} \right) +} \\\left( {\Delta \; {R^{2}/4}} \right)\end{matrix}}{\left( {R^{2}/4} \right) + L^{2}}} - 1} \right)}} \\{\approx {2 \cdot \sqrt{\left( {R^{2}/4} \right) + L^{2}} \cdot \frac{1}{2} \cdot \frac{\begin{matrix}{\left( {{R \cdot \Delta}\; {R/2}} \right) +} \\\left( {\Delta \; {R^{2}/4}} \right)\end{matrix}}{\left( {R^{2}/4} \right) + L^{2}}}} \\{\approx \frac{\left( {{R \cdot \Delta}\; {R/2}} \right)}{\sqrt{\left( {R^{2}/4} \right) + L^{2}}}} \\{\approx {\Delta \; R}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 177} \right\rbrack\end{matrix}$

Thus, it can be understood that the same channel difference ΔR=d²/(2R)as those obtained between the direct waves can be obtained and,accordingly, the phase rotation resulting from the channel difference isthe same (phase rotation (α=(π/λ)·(d²/R)). However, in terms of theabsolute phase, the channel difference in the case of the groundreflected wave is represented by the following formula.

$\begin{matrix}\begin{matrix}{{\Delta \; R_{abs}} = {2 \cdot \left( {\sqrt{\left( \frac{R}{2} \right)^{2} + L^{2}} - \left( \frac{R}{2} \right)} \right)}} \\{= {2 \cdot \left( \frac{R}{2} \right) \cdot \left( {\sqrt{1 + \left( \frac{2 \cdot L}{R} \right)^{2}} - 1} \right)}} \\{\approx {\left( \frac{R}{2} \right) \cdot \left( \frac{2 \cdot L}{R} \right)^{2}}} \\{\approx \frac{2 \cdot L^{2}}{R}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 178} \right\rbrack\end{matrix}$

Further, in terms of the absolute phase, the phase difference in thecase of the ground reflected wave is represented by the followingformula.

$\begin{matrix}{\alpha_{abs} \approx {4 \cdot \frac{\pi}{\lambda} \cdot \frac{L^{2}}{R}}} & \left\lbrack {{Numeral}\mspace{14mu} 179} \right\rbrack\end{matrix}$

Based on the above results, a reception signal vector Y is representedby the following formula.

$\begin{matrix}\begin{matrix}{Y = {U^{H} \cdot \left( {H + {a \cdot H \cdot ^{{- j}\; \alpha_{abs}}}} \right) \cdot V \cdot X}} \\{= {U^{H} \cdot \left( {{U \cdot \Lambda^{1/2} \cdot V^{H}} + {U \cdot \Lambda^{1/2} \cdot V^{H} \cdot ^{{- j}\; \alpha_{abs}}}} \right) \cdot}} \\{{V \cdot X}} \\{= {\left( {\Lambda^{1/2} + {a \cdot \Lambda^{1/2} \cdot ^{{- j}\; \alpha_{abs}}}} \right) \cdot X}} \\{{= \begin{bmatrix}{\lambda_{1} \cdot \left( {1 + {a \cdot ^{{- j}\; \alpha_{abs}}}} \right)} & 0 \\0 & {\lambda_{2} \cdot \left( {1 + {a \cdot ^{{- j}\; \alpha_{abs}}}} \right)}\end{bmatrix}} \cdot} \\{\begin{bmatrix}x_{1} \\x_{2}\end{bmatrix}} \\{= \begin{bmatrix}{\lambda_{1} \cdot \left( {1 + {a \cdot ^{{- j}\; \alpha_{abs}}}} \right) \cdot x_{1}} \\{\lambda_{2} \cdot \left( {1 + {a \cdot ^{{- j}\; \alpha_{abs}}}} \right) \cdot x_{2}}\end{bmatrix}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 180} \right\rbrack\end{matrix}$

where a denotes the reflection coefficient of the ground.

The above result reveals that, in the case of the configuration wherethe MIMO antennas are horizontally arranged, even if the groundreflected wave is present, orthogonality constructed by the MIMO ismaintained irrespective of the antenna height L from the ground.

In the case where the matrix calculation is performed only on thereception side, V=I is satisfied.

The above can be summarized as follows.

In the case of the configuration where the MIMO antennas arehorizontally arranged, even if the ground reflected wave is present,orthogonality constructed by the MIMO is ensured irrespective of theantenna height L.

[Case where MIMO Antennas are Vertically Arranged]

An example in which the MIMO antennas are vertically arranged in thetwo-ray model composed of the ground reflected wave and direct wave isshown in FIG. 21. In FIG. 21, the upper lines represent the direct wave,lower lines represent the ground reflected wave, and double linesrepresent a diagonal channel in the MIMO. In the case of theconfiguration where the MIMO antennas are vertically arranged, all thewaves pass on the straight lines set between the transmission andreception stations. Therefore, this configuration can be representedonly by an edge-on view. FIG. 22 shows the arrangement of FIG. 21 asviewed from directly above (upper part) and as viewed edge-on (lowerpart).

For characteristic analysis of the configuration where the MIMO antennasare vertically arranged, a mirror image model of FIG. 23 is also used.As shown in FIG. 23, the wave reflected by the ground looks as if itwere emitted from the mirror image. It is assumed in FIG. 23 that theMIMO antennas are arranged so that the virtual orthogonal channels canbe formed by the matrix calculation performed only for the direct wave.

That is, it is assumed that, with respect to the channel differenceΔR=d²/(2R) between the direct waves, the phase rotation a resulting fromthe channel difference has the relationship: α=(π/λ)·(d²/R)=π/2, and thematrix calculation is processed in accordance with the direct wave.

The configuration between the transmission station in the mirror imageand reception station corresponds to the abovementioned configuration inwhich antenna arrangement between transmission/reception sides is formedin diamond shape, and assuming that α=(π/λ)·(d²/R)=π/2,ζ=−(π/γ)·(2·d·L/R) is satisfied, the channel matrix H in this case isrepresented as the following formula.

$\begin{matrix}{H = \begin{bmatrix}1 & {^{{- j}\; \alpha} \cdot ^{j\; \xi}} \\{^{{- j}\; \alpha} \cdot ^{{- j}\; \xi}} & 1\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 181} \right\rbrack\end{matrix}$

It should be noted that in this case a directly opposing wave and acrossing wave are replaced by each other.

Based on the above formula, the phase difference (π/2) between thedirectly opposing wave and crossing wave in the ground reflected wavewill be examined From the upper-right element of the channel matrix H,the following formula can be obtained with the sign inversed (since thedirectly opposing wave and crossing wave are replaced by each other).

$\begin{matrix}{{{\alpha - \xi} = {{2\; \pi \; p} - \frac{\pi}{2}}}{where}{{p = 1},2,\ldots}} & \left\lbrack {{Numeral}\mspace{14mu} 182} \right\rbrack\end{matrix}$

Similarly, from the lower-left element of the channel matrix H, thefollowing formula can be obtained with the sign inversed.

$\begin{matrix}{{{\alpha + \xi} = {{2\; \pi \; q} - \frac{\pi}{2}}}{where}{{q = 1},2,\ldots}} & \left\lbrack {{Numeral}\mspace{14mu} 183} \right\rbrack\end{matrix}$

The difference between [Numeral 182] and [Numeral 183] is represented bythe following formula.

−ξ=πr where r=1,2, . . .   [Numeral 184]

From α=(π/λ)·(d²/R)=π/2, d=(λR/2)^(1/2) can be derived, so that thefollowing formula can be obtained.

$\begin{matrix}\begin{matrix}{\xi = {{- \frac{\pi}{\lambda}} \cdot \frac{2\; {dL}}{R}}} \\{= {{- \frac{\pi}{\lambda}} \cdot \frac{2\; L}{R} \cdot \sqrt{\frac{\lambda \; R}{2}}}} \\{= {{- \pi} \cdot \sqrt{\frac{2}{\lambda \; R}} \cdot L}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 185} \right\rbrack\end{matrix}$

Accordingly, from −π=−π·(λR/2)^(1/2)·L the following formula can beobtained.

$\begin{matrix}{{L = {{\sqrt{\frac{\lambda \; R}{2}} \cdot r} = {d \cdot r}}}{where}{{r = 1},2,\ldots}} & \left\lbrack {{Numeral}\mspace{14mu} 186} \right\rbrack\end{matrix}$

That is, in the case where the MIMO antennas are vertically arranged, inorder to allow the phase difference π/2 between the directly opposingwave and crossing wave with respect to the direct wave to be appliedwithout modification to the delayed wave, it is necessary to make theantenna height L from the ground an integral multiple of the antennainterval d in the MIMO configuration.

In the following, it is assumed that the antenna height L from theground is made an integral multiple of d.

[Case where MIMO Antennas are Vertically Arranged Under Condition whereL=n·d is Satisfied]

The results thus obtained are summarized as an analysis model of FIG.24. This model is used to perform the following calculation.

1) Channel Difference (Crossing Wave−Directly Opposing Wave) in R#1

$\begin{matrix}{{\frac{\left( {{2\; n} + 1} \right)^{2}d^{2}}{2\; R} - \frac{\left( {{2\; n} + 2} \right)^{2}d^{2}}{2\; R}} = {{- \left( {{4\; n} + 3} \right)}\frac{d^{2}}{2\; R}}} & \left\lbrack {{Numeral}\mspace{14mu} 187} \right\rbrack \\\begin{matrix}{{{Phase}\mspace{14mu} {difference}} = {\frac{2\; \pi}{\lambda}\left( {{- \left( {{4\; n} + 3} \right)}\frac{d^{2}}{2\; R}} \right)}} \\{= {{- \left( {{4\; n} + 3} \right)}\frac{\pi}{2}}} \\{\equiv {\frac{\pi}{2}\left( {{mod}\mspace{14mu} 2\; \pi} \right)}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 188} \right\rbrack\end{matrix}$

2) Channel Difference (Crossing Wave−Directly Opposing Wave) in R#2

$\begin{matrix}{{\frac{\left( {{2\; n} + 1} \right)^{2}d^{2}}{2\; R} - \frac{\left( {2\; n} \right)^{2}d^{2}}{2\; R}} = {\left( {{4\; n} + 1} \right)\frac{d^{2}}{2\; R}}} & \left\lbrack {{Numeral}\mspace{14mu} 189} \right\rbrack \\\begin{matrix}{{{Phase}\mspace{14mu} {difference}} = {\frac{2\; \pi}{\lambda}\left( {\left( {{4\; n} + 1} \right)\frac{d^{2}}{2\; R}} \right)}} \\{= {\left( {{4\; n} + 1} \right)\frac{\pi}{2}}} \\{\equiv {\frac{\pi}{2}\left( {{mod}\mspace{14mu} 2\; \pi} \right)}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 190} \right\rbrack\end{matrix}$

Further, whether the phase difference resulting from the channeldifference between directly opposing waves is 2π n or not is checked.

3) Check whether phase difference resulting from channel differencebetween same directly opposing waves is 0 mod(2π)

$\begin{matrix}{{\frac{\left( {{2\; n} + 2} \right)^{2}d^{2}}{2\; R} - \frac{\left( {2\; n} \right)^{2}d^{2}}{2\; R}} = {\left( {{8\; n} + 4} \right)\frac{d^{2}}{2\; R}}} & \left\lbrack {{Numeral}\mspace{14mu} 191} \right\rbrack \\\begin{matrix}{{{Phase}\mspace{14mu} {difference}} = {\frac{2\; \pi}{\lambda}\left( {\left( {{8\; n} + 4} \right)\frac{d^{2}}{2\; R}} \right)}} \\{= {\left( {{8\; n} + 4} \right)\frac{\pi}{2}}} \\{\equiv {0\; \left( {{mod}\mspace{14mu} 2\; \pi} \right)}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 192} \right\rbrack\end{matrix}$

Further, when the channel difference is ΔR_(ab), the absolute phaseα_(abs) is represented by the following formula (T#1−R#1 is taken as arepresentative example).

$\begin{matrix}{{\Delta \; R_{abs}} = \frac{\left( {{2\; n} + 2} \right)^{2}d^{2}}{2\; R}} & \left\lbrack {{Numeral}\mspace{14mu} 193} \right\rbrack\end{matrix}$

The absolute phase is represented as follows.

$\begin{matrix}{\alpha_{abs} = {\frac{2\; \pi}{\lambda}\left( \frac{\left( {{2\; n} + 2} \right)^{2}d^{2}}{2\; R} \right)\left( {{mod}\mspace{14mu} 2\; \pi} \right)}} & \left\lbrack {{Numeral}\mspace{14mu} 194} \right\rbrack\end{matrix}$

The channel matrix H_(reflection) with respect to the ground reflectedwave in the configuration (L=n·d) where the MIMO antennas are verticallyarranged, which is calculated based on the above results, is representedby the following formula.

$\begin{matrix}\begin{matrix}{H_{reflection} = {a \cdot \begin{bmatrix}^{{- j}\; 0} & ^{{- j}\frac{\pi}{2}} \\^{{- j}\frac{\pi}{2}} & ^{{- j}\; 0}\end{bmatrix} \cdot ^{{- j}\; \alpha_{abs}}}} \\{= {a \cdot \begin{bmatrix}1 & {- j} \\{- j} & 1\end{bmatrix} \cdot ^{{- j}\; \alpha_{abs}}}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 195} \right\rbrack\end{matrix}$

where a denotes the reflection coefficient of the ground.

The channel matrix H with respect to the direct wave is represented bythe following formula.

$\begin{matrix}{H = \begin{bmatrix}1 & {- j} \\{- j} & 1\end{bmatrix}} & \left\lbrack {{Numeral}\mspace{14mu} 196} \right\rbrack\end{matrix}$

Accordingly, the following formula can be obtained.

H _(reflection) =a·H·e ^(−jα) ^(abs)   [Numeral 197]

The following formula can be obtained as the reception signal vector Ybased on the above calculation result.

$\begin{matrix}\begin{matrix}{Y = {U^{H} \cdot \left( {H + {a \cdot H \cdot ^{{- j}\; \alpha_{abs}}}} \right) \cdot V \cdot X}} \\{= {U^{H} \cdot \left( {{U \cdot \Lambda^{1/2} \cdot V^{H}} + {U \cdot \Lambda^{1/2} \cdot V^{H} \cdot ^{{- j}\; \alpha_{abs}}}} \right) \cdot}} \\{{V \cdot X}} \\{= {\left( {\Lambda^{1/2} + {a \cdot \Lambda^{1/2} \cdot ^{{- j}\; \alpha_{abs}}}} \right) \cdot X}} \\{= {\begin{bmatrix}{\lambda_{1} \cdot \left( {1 + {a \cdot ^{{- j}\; \alpha_{abs}}}} \right)} & 0 \\0 & {\lambda_{2} \cdot \left( {1 + {a \cdot ^{{- j}\; \alpha_{abs}}}} \right)}\end{bmatrix} \cdot}} \\{\begin{bmatrix}x_{1} \\x_{2}\end{bmatrix}} \\{= \begin{bmatrix}{\lambda_{1} \cdot \left( {1 + {a \cdot ^{{- j}\; \alpha_{abs}}}} \right) \cdot x_{1}} \\{\lambda_{2} \cdot \left( {1 + {a \cdot ^{{- j}\; \alpha_{abs}}}} \right) \cdot x_{2}}\end{bmatrix}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 198} \right\rbrack\end{matrix}$

where a denotes the reflection coefficient of the ground.

That is, it can be understood that in the case where the reflected wavefrom the ground is present in the configuration where the MIMO antennasare vertically arranged, if the relationship L=n·d is satisfied for theantenna height L from the ground, the orthogonality constructed by theMIMO is maintained.

In the case where the matrix calculation is performed only on thereception side, V=I is satisfied.

The above can be summarized as follows. That is, in the case of theconfiguration where the MIMO antennas are vertically arranged, even ifthe ground reflected wave is present, orthogonality constructed by theMIMO is ensured as long as the antenna height L is made an integralmultiple (L=n·d) of the antenna interval d.

[Robustness in Case where MIMO Antennas are Horizontally Arranged]

Next, robustness in the case where the MIMO antennas are horizontallyarranged will be described.

The above discussion has been made based on the assumption that theground is flat. Under the actual condition, it is likely that the groundis roughened, as shown in FIG. 25. In this case, the reflectioncoefficient a of the ground acts as the average behavior of thereflected wave. However, in the following, a case, as shown in FIG. 26,where there unfortunately exist irregular reflecting objects will bedescribed. FIG. 27 is an analysis model used for this description andfocuses on a given i-th irregular reflecting object without losinggenerality.

It is assumed, from the abovementioned relationship, that with respectto the channel difference ΔR=d²/(2R) between the direct waves, the phaserotation a resulting from the channel difference has the relationship:α=(π/λ)·(d²/R)=π/2 (orthogonal condition). From the relationship shownin FIG. 27, the channel difference ΔR_(refi) between given i-thirregular reflected waves is represented by the following formula.

$\begin{matrix}\begin{matrix}{{\Delta \; R_{{ref}\mspace{11mu} i}} = {\sqrt{{m^{2}\left( {R + {\Delta \; R}} \right)}^{2} + L^{2}} +}} \\{{\sqrt{{\left( {1 - m} \right)^{2}\left( {R + {\Delta \; R}} \right)^{2}} + L^{2}} - \sqrt{{m^{2}R^{2}} + L^{2}} -}} \\{\sqrt{{\left( {1 - m} \right)^{2}R^{2}} + L^{2}}} \\{= {{\sqrt{{m^{2}R^{2}} + L^{2}}\left( {\sqrt{1 + \frac{\begin{matrix}{{m^{2}2\; {R \cdot \Delta}\; R} +} \\{{m^{2} \cdot \Delta}\; R^{2}}\end{matrix}}{{m^{2}R^{2}} + L^{2}}} - 1} \right)} +}} \\{{\sqrt{{\left( {1 - m} \right)^{2}R^{2}} + L^{2}}\left( {\sqrt{1 + \frac{\begin{matrix}{\left( {1 - m} \right)^{2}2{R \cdot}} \\{{\Delta \; R} +} \\{\left( {1 - m} \right)^{2} \cdot} \\{\Delta \; R^{2}}\end{matrix}}{{\left( {1 - m} \right)^{2}R^{2}} + L^{2}}} - 1} \right)}} \\{\approx {{\sqrt{{m^{2}R^{2}} + L^{2}}\left( \frac{\begin{matrix}{{m^{2}\; {R \cdot \Delta}\; R} +} \\{{m^{2} \cdot \Delta}\; R^{2}}\end{matrix}}{{m^{2}R^{2}} + L^{2}} \right)} +}} \\{{\sqrt{{\left( {1 - m} \right)^{2}R^{2}} + L^{2}}\left( \frac{\begin{matrix}{{\left( {1 - m} \right)^{2}{R \cdot \Delta}\; R} +} \\{{\left( {1 - m} \right)^{2} \cdot \Delta}\; R^{2}}\end{matrix}}{{\left( {1 - m} \right)^{2}R^{2}} + L^{2}} \right)}} \\{\approx {\frac{{m^{2}{R \cdot \Delta}\; R} + {{m^{2} \cdot \Delta}\; R^{2}}}{\sqrt{{m^{2}R^{2}} + L^{2}}} + \frac{\begin{matrix}{{\left( {1 - m} \right)^{2}{R \cdot \Delta}\; R} +} \\{{\left( {1 - m} \right)^{2} \cdot \Delta}\; R^{2}}\end{matrix}}{\sqrt{{\left( {1 - m} \right)^{2}R^{2}} + L^{2}}}}} \\{\approx {{{m \cdot \Delta}\; R} + {{\left( {1 - m} \right) \cdot \Delta}\; R\; \left( {{{\therefore{mR}}\operatorname{>>}L},{{\left( {1 - m} \right)R}\operatorname{>>}L}} \right)}}} \\{\approx {\Delta \; R}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 199} \right\rbrack\end{matrix}$

(The reflecting object is assumed to be positioned at a distance of mafrom the transmission station and at a distance of (1−m)·R from thereception station). Thus, ΔR_(refi)=ΔR=d2/(2R) same as the channeldifference between the direct waves can be obtained.

Accordingly, the phase rotation resulting from the channel difference isrepresented by α=(π/λ)·(d²/R)=π/2 and thus the orthogonal condition issatisfied. Based on this result, a case where N reflecting objects existwill be considered.

Assuming that the phase differences with respect to the direct waves ofN reflecting objects are α_(abs0), . . . , α_(abs(N-1)), the receptionsignal vector Y is represented by the following formula.

$\begin{matrix}\begin{matrix}{Y = {{U^{H}\left( {H + {\sum\limits_{i = 0}^{N - 1}\; {a_{i}H\; ^{{- j}\; \alpha_{abs}}}}} \right)}{VX}}} \\{= {{U^{H}\left( {{U\; \Lambda^{1/2}V^{H}} + {\sum\limits_{i = 0}^{N - 1}\; {a_{i}U\; \Lambda^{1/2}V^{H}^{{- j}\; \alpha_{{abs}\mspace{11mu} i}}}}} \right)}{VX}}} \\{= {\left( {\Lambda^{1/2} + {\sum\limits_{i = 0}^{N - 1}\; {a_{i}\Lambda^{1/2}V^{H}^{{- j}\; \alpha_{{abs}\mspace{11mu} i}}}}} \right) \cdot X}} \\{= {\begin{bmatrix}{\lambda_{1}\begin{pmatrix}{1 +} \\{\sum\limits_{i = 0}^{N - 1}\; {a_{i}^{{- j}\; \alpha_{{abs}\mspace{11mu} i}}}}\end{pmatrix}} & 0 \\0 & \left. {\lambda_{2}\begin{pmatrix}{1 +} \\{\sum\limits_{i = 0}^{N - 1}\; {a_{i}^{{- j}\; \alpha_{{abs}\mspace{11mu} i}}}}\end{pmatrix}} \right)\end{bmatrix} \cdot}} \\{\begin{bmatrix}x_{1} \\x_{2}\end{bmatrix}} \\{= \begin{bmatrix}{{\lambda_{1}\left( {1 + {\sum\limits_{i = 0}^{N - 1}\; {a_{i}^{{- j}\; \alpha_{{abs}\mspace{11mu} i}}}}} \right)} \cdot x_{1}} \\{{\lambda_{2}\left( {1 + {\sum\limits_{i = 0}^{N - 1}\; {a_{i}^{{- j}\; \alpha_{{abs}\mspace{11mu} i}}}}} \right)} \cdot x_{2}}\end{bmatrix}}\end{matrix} & \left\lbrack {{Numeral}\mspace{14mu} 200} \right\rbrack\end{matrix}$

where a_(i) denotes the N-th reflection coefficient of the ground.

As shown by the above result, even if N irregular reflecting objectsexist, the orthogonal condition is satisfied. In the case where thematrix calculation is performed only on the reception side, V=I issatisfied.

The results thus obtained are summarized. That is, in the case where theMIMO antennas are horizontally arranged, even if a plurality ofirregular reflected waves from the ground exist, the orthogonalityformed by the MIMO can be ensured and is robust.

The advantages and defects in the respective configurations thusobtained are summarized as follows.

1. Case where MIMO Antennas are Horizontally Arranged

[Advantage]

-   -   Orthogonality of MIMO channels including ground reflected wave        is ensured irrespective of antenna installation height.    -   Orthogonality is robust against irregular reflected wave from        ground.

[Defect]

-   -   Horizontal axis support is required for antenna installation

2. Case where MIMO Antennas are Vertically Arranged

[Advantage]

-   -   Antenna installation structure can be simplified due to vertical        arrangement, thereby achieving space saving.

[Defect]

-   -   Antenna installation height L is limited to L=n·d (d is MIMO        antenna interval) where n=1, 2, . . . .

The above-described respective configurations where the reflected wavehas been taken into consideration are not limited to the individualexamples but may be combined with any of the configurations where thereflected wave has not been taken into consideration.

The exemplary embodiment and examples of the present invention have beendescribed above, and, in the following, preferred embodiments of thepresent invention are listed below.

First Exemplary Embodiment

A MIMO communication system having deterministic channels and an antennaarrangement method for the system includes a channel matrix calculationprocessing section on a transmission or reception side or both of thetransmission and reception sides in a MIMO communication system used ina line-of-sight environment. The channel matrix calculation processingsection updates an orthogonal channel formation matrix in accordancewith a positional variation of a transmission antenna or receptionantenna, positional variations of both of the transmission and receptionantennas, or a variation of the channels. A plurality of transmissionantennas and a plurality of reception antennas constituting the channelmatrix are horizontally arranged with respect to the ground.

With this configuration, when a positional variation of a transmissionantenna or reception antenna or a variation of the channels iscompensated in the channel matrix calculation processing section, it ispossible to absorb the positional variation of a transmission antenna orreception antenna or variation of the channels even if a reflected waveother than the direct wave is present during line-of-sightcommunication, thereby ensuring orthogonality.

Second Exemplary Embodiment

A MIMO communication system having deterministic channels and an antennaarrangement method for the system includes a channel matrix calculationprocessing section on a transmission or reception side or both of thetransmission and reception sides in a MIMO communication system used ina line-of-sight environment. The channel matrix calculation processingsection updates an orthogonal channel formation matrix in accordancewith a positional variation of a transmission antenna or receptionantenna, positional variations of both of the transmission and receptionantennas, or a variation of the channels. A plurality of transmissionantennas and a plurality of reception antennas constituting the channelmatrix are vertically arranged with respect to the ground. The antennaheight from the ground is made an integral multiple of the antennainterval.

With this configuration, when a positional variation of a transmissionantenna or reception antenna or a variation of the channels iscompensated in the channel matrix calculation processing section, it ispossible to absorb the positional variation of a transmission antenna orreception antenna or variation of the channels in an antennaconfiguration where space saving is achieved due to vertical arrangementof the antennas even if a reflected wave other than the direct wave ispresent during line-of-sight communication, thereby ensuringorthogonality.

Third Exemplary Embodiment

A MIMO communication system having deterministic channels and an antennaarrangement method for the system set geometric parameters of thechannels so that the eigenvalue of the channel matrix becomes amultiplicity condition and perform calculation of a unitary matrixconstituted based on an eigenvector obtained from the eigenvalue or aneigenvector obtained from the linear combination of eigenvectors on oneof the transmission and reception sides to thereby construct virtualorthogonal channels. A plurality of transmission antennas and aplurality of reception antennas constituting the channel matrix arehorizontally arranged with respect to the ground.

With this configuration, even if a reflected wave other than the directwave is present during line-of-sight communication, it is possible toachieve flexible design of a system having a configuration where thereis no need to use a reverse channel for exchanging feedback informationand a configuration where only transmission processing is performedwhile ensuring orthogonality.

Fourth Exemplary Embodiment

A MIMO communication system having deterministic channels and an antennaarrangement method for the system set geometric parameters of thechannels so that the eigenvalue of the channel matrix becomes amultiplicity condition and perform calculation of a unitary matrixconstituted based on an eigenvector obtained from the eigenvalue or aneigenvector obtained from the linear combination of eigenvectors on oneof the transmission and reception sides to thereby construct virtualorthogonal channels. A plurality of transmission antennas and aplurality of reception antennas constituting the channel matrix arevertically arranged with respect to the ground. The antenna height fromthe ground is made an integral multiple of the antenna interval.

With this configuration, even if a reflected wave other than the directwave is present during line-of-sight communication, it is possible toachieve flexible design of a system having a configuration where thereis no need to use a reverse channel for exchanging feedback informationand a configuration where only transmission processing is performedwhile ensuring orthogonality in an antenna configuration where spacesaving is achieved due to vertical arrangement of the antennas.

Fifth Exemplary Embodiment

In a MIMO communication system having deterministic channels and anantenna arrangement method for the system, the MIMO communication systemis a fixed point microwave communication system using a plurality ofantennas and constituted by using local oscillators providedindependently for respective antennas on one or both of the transmissionand reception sides. A plurality of transmission antennas and aplurality of reception antennas constituting the channel matrix arehorizontally arranged with respect to the ground.

With this configuration, even if a reflected wave other than the directwave is present during line-of-sight communication, it is possible tosolve the problem of the necessity of achievement of carriersynchronization between antennas that imposes restriction onconstruction of the MIMO communication system for the fixed pointmicrowave communication system.

Sixth Exemplary Embodiment

In a MIMO communication system having deterministic channels and anantenna arrangement method for the system, the MIMO communication systemis a fixed point microwave communication system using a plurality ofantennas and constituted by using local oscillators providedindependently for respective antennas on one or both of the transmissionand reception sides. A plurality of transmission antennas and aplurality of reception antennas constituting the channel matrix arevertically arranged with respect to the ground. The antenna height fromthe ground is made an integral multiple of the antenna interval.

With this configuration, even if a reflected wave other than the directwave is present during line-of-sight communication, it is possible tosolve the problem of the necessity of achievement of carriersynchronization between antennas that imposes restriction onconstruction of the MIMO communication system for the fixed pointmicrowave communication system in an antenna configuration where spacesaving is achieved due to vertical arrangement of the antennas.

Seventh Exemplary Embodiment

A MIMO communication system used in a line-of-sight environment hasdeterministic channels between the transmission side where a pluralityof transmission antennas are arranged and the reception side where aplurality of reception antennas are arranged. A transmitter of the MIMOcommunication system has a channel matrix calculation processing meansfor calculating a channel matrix for constructing orthogonal channels asthe channels. A plurality of transmission antennas constituting thechannel matrix are horizontally arranged.

Eighth Exemplary Embodiment

A MIMO communication system used in a line-of-sight environment hasdeterministic channels between the transmission side where a pluralityof transmission antennas are arranged and the reception side where aplurality of reception antennas are arranged. A transmitter of the MIMOcommunication system has a channel matrix calculation processing meansfor calculating a channel matrix for constructing orthogonal channels asthe channels. A plurality of transmission antennas constituting thechannel matrix are vertically arranged with respect to the ground. Theantenna height from the ground is made an integral multiple of theantenna interval.

Ninth Exemplary Embodiment

A MIMO communication system has deterministic channels between thetransmission side where a plurality of transmission antennas arearranged and the reception side where a plurality of reception antennasare arranged. A transmitter of the MIMO communication system has achannel matrix calculation processing means for constructing orthogonalchannels as the channels by setting geometric parameters of the channelsconcerning antenna interval so that the eigenvalue of the channel matrixbecomes a multiplicity condition and performing matrix calculation usinga unitary matrix constituted based on singular vectors obtained from theeigenvalue or singular vectors obtained from the linear combination ofeigenvectors. A plurality of transmission antennas constituting thechannels are horizontally arranged with respect to the ground.

Tenth Exemplary Embodiment

A MIMO communication system has deterministic channels between thetransmission side where a plurality of transmission antennas arearranged and the reception side where a plurality of reception antennasare arranged. A transmitter of the MIMO communication system has achannel matrix calculation processing means for constructing orthogonalchannels as the channels by setting geometric parameters of the channelsconcerning antenna interval so that the eigenvalue of the channel matrixbecomes a multiplicity condition and performing matrix calculation usinga unitary matrix constituted based on singular vectors obtained from theeigenvalue or singular vectors obtained from the linear combination ofeigenvectors. A plurality of transmission antennas constituting thechannels are vertically arranged with respect to the ground. The antennaheight from the ground is made an integral multiple of the antennainterval.

Eleventh Exemplary Embodiment

A MIMO communication system used in a line-of-sight environment hasdeterministic channels between the transmission side where a pluralityof transmission antennas are arranged and the reception side where aplurality of reception antennas are arranged. A receiver of the MIMOcommunication system has a channel matrix calculation processing meansfor calculating a channel matrix for constructing orthogonal channels asthe channels. A plurality of reception antennas constituting the channelmatrix are horizontally arranged with respect to the ground.

Twelfth Exemplary Embodiment

A MIMO communication system used in a line-of-sight environment hasdeterministic channels between the transmission side where a pluralityof transmission antennas are arranged and the reception side where aplurality of reception antennas are arranged. A receiver of the MIMOcommunication system has a channel matrix calculation processing meansfor calculating a channel matrix for constructing orthogonal channels asthe channels. A plurality of reception antennas constituting the channelmatrix are vertically arranged with respect to the ground. The antennaheight from the ground is made an integral multiple of the antennainterval.

Thirteenth Exemplary Embodiment

A MIMO communication system has deterministic channels between thetransmission side where a plurality of transmission antennas arearranged and the reception side where a plurality of reception antennasare arranged. A receiver of the MIMO communication system has a channelmatrix calculation processing means for constructing orthogonal channelsas the channels by setting geometric parameters of the channelsconcerning antenna interval so that the eigenvalue of the channel matrixbecomes a multiplicity condition and performing matrix calculation usinga unitary matrix constituted based on singular vectors obtained from theeigenvalue or singular vectors obtained from the linear combination ofeigenvectors. A plurality of reception antennas constituting thechannels are horizontally arranged with respect to the ground.

Fourteenth Exemplary Embodiment

A MIMO communication system has deterministic channels between thetransmission side where a plurality of transmission antennas arearranged and the reception side where a plurality of reception antennasare arranged. A receiver of the MIMO communication system has a channelmatrix calculation processing means for constructing orthogonal channelsas the channels by setting geometric parameters of the channelsconcerning antenna interval so that the eigenvalue of the channel matrixbecomes a multiplicity condition and performing matrix calculation usinga unitary matrix constituted based on singular vectors obtained from theeigenvalue or singular vectors obtained from the linear combination ofeigenvectors. A plurality of reception antennas constituting thechannels are vertically arranged with respect to the ground. The antennaheight from the ground is made an integral multiple of the antennainterval.

The transmitter and receiver constituting the MIMO communication systemare not especially limited in terms of their hardware and softwareconfiguration but may have any configuration as long as they can realizethe functions (means) of the respective components. For example, aconfiguration in which circuits are independently provided for eachfunction, or configuration in which a plurality of functions areintegrated in one circuit may be adopted. Alternatively, a configurationin which all functions are realized by software processing may beadopted. In the case where the above functions are realized throughsoftware processing controlled by a CPU (Central Processing Unit), aprogram executed in a computer and a computer-readable recording mediumstoring the program belong to the scope of the present invention.

Although the present invention has been described with reference to theexemplary embodiments and examples, the present invention is not limitedto the above exemplary embodiments and examples, and it is apparent tothose skilled in the art that a variety of modifications and changes maybe made to the configurations and details of the present inventionwithout departing from the scope of the present invention.

This application is based upon and claims the benefit of priority fromprior Japanese Patent Application No. 2007-201773 (filed on Aug. 2,2007), the entire contents of which are incorporated herein byreference.

INDUSTRIAL APPLICABILITY

The present invention can be applied to a MIMO communication system suchas a fixed point microwave communication system having deterministicchannels between the transmission side where a plurality of transmissionantennas are provided and reception side where a plurality of receptionantennas are provided, an antenna arrangement method therefore, atransmitter thereof and a receiver thereof.

1. A MIMO communication system having deterministic channels between thetransmission side where a plurality of transmission antennas arearranged and the reception side where a plurality of reception antennasare arranged and used in a line-of-sight environment, the systemcomprising channel matrix calculation processing means for calculating achannel matrix for constructing orthogonal channels as the channel on atransmission or reception side or both of the transmission and receptionsides, wherein the plurality of transmission antennas and plurality ofreception antennas constituting the channel matrix are horizontallyarranged with respect to the ground.
 2. The MIMO communication systemhaving deterministic channels according to claim 1, wherein the channelmatrix calculation processing means updates a channel matrix forconstructing the orthogonal channels in accordance with a positionalvariation of a transmission antenna or reception antenna, positionalvariations of both of the transmission and reception antennas, or avariation of the channels.
 3. The MIMO communication system havingdeterministic channels according to claim 1, wherein the MIMOcommunication system comprises a fixed point microwave communicationsystem using a plurality of antennas and is constituted by using localoscillators provided independently for respective antennas on one orboth of the transmission and reception sides.
 4. An antenna arrangementmethod for a MIMO communication system having deterministic channelsbetween the transmission side where a plurality of transmission antennasare arranged and the reception side where a plurality of receptionantennas are arranged and used in a line-of-sight environment, themethod comprising channel matrix calculation processing means forcalculating a channel matrix for constructing orthogonal channels as thechannel on a transmission or reception side or both of the transmissionand reception sides, wherein the plurality of transmission antennas andplurality of reception antennas constituting the channel matrix arehorizontally arranged with respect to the ground.
 5. A receiver of aMIMO communication system having deterministic channels between thetransmission side where a plurality of transmission antennas arearranged and the reception side where a plurality of reception antennasare arranged and used in a line-of-sight environment, the receivercomprising channel matrix calculation processing means for calculating achannel matrix for constructing orthogonal channels as the channel,wherein the plurality of reception antennas constituting the channelmatrix are horizontally arranged with respect to the ground.